arXiv subjects

D. Yang

Publications and source records attributed to D. Yang.

23 records · Page 2Linked to original sources

arXiv2010

A Novel Approach to Elastodynamics: I. The Two-Dimensional Case

We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and Lamb's boundary conditions. A particular case of this problem, namely the case of homogeneous initial conditions, was first solved by Lamb using the Fourier-Laplace transform. The solution of the general problem can also be expressed in terms of the Fourier transform, but this representation involves transforms of unknown boundary values. This necessitates the formulation and solution of a cumbersome auxiliary problem, which expresses the unknown boundary values in terms of the Laplace transform of the given boundary data. The new approach, which is applicable to arbitrary initial and boundary conditions, bypasses the above auxiliary problem and expresses the solutions directly in terms of the given initial and boundary data.

math.AP↗

arXiv2010

A Novel Approach to Elastodynamics: II. The Three-Dimensional Case

A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying arbitrary initial conditions and Lamb's boundary conditions. A particular case of this problem, namely the case of homogeneous initial conditions and normal point load boundary conditions, was first solved by Lamb using the Fourier-Laplace transform. The general problem solved here can also be analysed via the Fourier transform, but in this case, the solution representation involves transforms of \textit{unknown} boundary values; this necessitates the formulation and solution of a cumbersome auxiliary problem, which expresses the unknown boundary values in terms of the Laplace transform of the given boundary data. The new approach, which is applicable to arbitrary initial and boundary conditions, bypasses the above auxiliary problem and expresses the solutions directly in terms of the given initial and boundary conditions.

math.AP↗

arXiv2010

On a Novel Class of Integrable ODEs Related to the Painlevé Equations

One of the authors has recently introduced the concept of conjugate Hamiltonian systems: the solution of the equation $h=H(p,q,t),$ where $H$ is a given Hamiltonian containing $t$ explicitly, yields the function $t=T(p,q,h)$, which defines a new Hamiltonian system with Hamiltonian $T$ and independent variable $h.$ By employing this construction and by using the fact that the classical Painlevé equations are Hamiltonian systems, it is straightforward to associate with each Painlevé equation two new integrable ODEs. Here, we investigate the conjugate Painlevé II equations. In particular, for these novel integrable ODEs, we present a Lax pair formulation, as well as a class of implicit solutions. We also construct conjugate equations associated with Painlevé I and Painlevé IV equations.

nlin.SI↗

arXiv2005

Enhanced electroweak penguin amplitude in B-->VV decays

We discuss a novel electromagnetic penguin contribution to the transverse helicity amplitudes in B decays to two vector mesons, which is enhanced by two powers of mB/Lambda relative to the standard penguin amplitudes. This leads to unique polarization signatures in penguin-dominated decay modes such as B-->rho K* similar to polarization effects in the radiative decay B-->K*gamma, and offers new opportunities to probe the magnitude and chirality of flavour-changing neutral current couplings to photons.

hep-ph↗

arXiv2005

Heavy-to-light B meson form factors at large recoil energy -- spectator-scattering corrections

We complete the investigation of loop corrections to hard spectator-scattering in exclusive B meson to light meson transitions by computing the short-distance coefficient (jet-function) from the hard-collinear scale. Adding together the two coefficients from matching QCD to SCET_I to SCET_II, we investigate the size of loop effects on the ratios of heavy-to-light meson form factors at large recoil. We find the corrections from the hard and hard-collinear scales to be of approximately the same size, and significant, but the perturbative expansions appear to be well-behaved. Our calculation provides a non-trivial verification of the factorization arguments. We observe considerable differences between the predictions based on factorization in the heavy-quark limit and current QCD sum rule calculations of the form factors. We also include the hard-collinear correction in the B -> pi pi tree amplitudes, and find an enhancement of the colour-suppressed amplitude relative to the colour-allowed amplitude.

hep-ph↗