1,720,964 research outputs found
Memory Effects on Nonlinear Temperature and Pressure Wave Propagation in the Boundary between Two Fluid-Saturated Porous Rocks
No full textOn isochronous Shabat-Yamilov lattices: equilibrium configurations, behavior in their neighborhood, diophantine relations and conjectures
No full textIsochronous variant of the Ruijsenaars-Toda model: equilibrium configuration, behavior in their neighborhood, Diophantine relations
No full textGli articoli su questa rivista (e molte altre) vengono ora identificati con un numero e con la indicazione del numero di pagine
Integrability, analyticity, isochrony, equilibria, small oscillations, and Diophantine relations: results from the stationary KdV hierarchy
No full textThe isochronous variant is exhibited of the dynamical system corresponding to the Mth ordinary differential equation of the stationary Korteweg-de Vries (KdV) hierarchy. New Diophantine relations are thereby obtained, in the guise of matrices of arbitrary order having integer eigenvalues or equivalently of polynomials of arbitrary degree having integer zeros. Generalizations of these formulas to relations among rational functions are also obtained. The basic idea to arrive at such relations is not new, but the specific application reported in this paper is new, and it is likely to open the way to several analogous new findings
An isochronous variant of the Ruijsenaars-Toda model: equilibrium configurations, behavior in their neighborhood, Diophantine relations
No full textAn isochronous variant of the Ruijsenaars-Toda integrable many-body problem is introduced, an equilibrium configuration of this dynamical system is identified and by investigating the motions in its neighborhood Diophantine relations are obtained
On the propagation of nonlinear transients of temperature and pore pressure in a thin porous boundary layer between two rocks
No full textThe dynamics of transients of fluid-rock temperature, pore pressure, pollutants in porous rocks are of vivid interest for fundamental problems in hydrological, volcanic, hydrocarbon systems, deep oil drilling. This can concern rapid landslides or the fault weakening during coseismic slips and also a new field of research about stability of classical buildings. Here we analyze the transient evolution of temperature and pressure in a thin boundary layer between two adjacent homogeneous media for various types of rocks. In previous models, this boundary was often assumed to be a sharp mathematical plane. Here we consider a non-sharp, physical boundary between two adjacent rocks, where also local steady pore pressure and/or temperature fields are present. To obtain a more reliable model we also investigate the role of nonlinear effects as convection and fluid-rock “frictions”, often disregarded in early models: these nonlinear effects in some cases can give remarkable quick and sharp transients. All of this implies a novel model, whose solutions describe large, sharp and quick fronts. We also rapidly describe transients moving through a particularly irregular boundary layer
Additional Recursion Relations, Factorizations, and Diophantine Properties Associated with the Polynomials of the Askey Scheme
No full textIn this paper, we apply to (almost) all the “named”
polynomials of the Askey scheme, as defined by their standard
three-term recursion relations, the machinery developed in
previous papers. For each of these polynomials we identify at
least one additional recursion relation involving a shift in some
of the parameters they feature, and for several of these
polynomials characterized by special values of their parameters,
factorizations are identified yielding some or all of their
zeros—generally given by simple expressions in terms of
integers (Diophantine
relations). The factorization findings generally are applicable
for values of the Askey polynomials that extend beyond those for
which the standard orthogonality relations hold. Most of these
results are not (yet) reported in the standard compilations
A Note on Exact Results for Burgers-like Equations Involving Laguerre Derivatives
No full textIn this work, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of variables. We prove that a general scheme exists for constructing exact solutions for these Burgers-like equations and extending to more general cases, including nonlinear time-fractional equations. Exact solutions can also be obtained for KDV-like equations involving Laguerre derivatives. We finally consider a particular class of Burgers equations with variable coefficients whose solutions can be obtained similarly
ESA Living Planet Symposium 2016 - Combination of multivariate satellite and in situ observations provides new insight on the 3D dynamics along the Antarctic Circumpolar Current
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