Related papers: Second order singular pertubative theory for gravi…
If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as…
Shape derivative is an important analytical tool for studying scattering problems involving perturbations in scatterers. Many applications, including inverse scattering, optimal design, and uncertainty quantification, are based on shape…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
When gravitational waves travel from their source to an observer, they interact with matter structures along their path, causing distinct deformations in their waveforms. In this study we introduce a novel theoretical framework for wave…
We account for all the image distortions relevant to weak gravitational lensing to second order. Besides the familiar shear, convergence, rotation and flexions, we find a new image distortion with two distinct descriptions, the twist and…
Policy gradient methods are a powerful family of reinforcement learning algorithms for continuous control that optimize a policy directly. However, standard first-order methods often converge slowly. Second-order methods can accelerate…
We present a method for constructing gauge-invariant cosmological perturbations which are gauge-invariant up to second order. As an example we give the gauge-invariant definition of the second-order curvature perturbation on uniform density…
When a luminous source is extended, its distortions by weak gravitational lensing are richer than a mere combination of magnification and shear. In a recent work, we proposed an elegant formalism based on complex analysis to describe and…
The newly developed single trajectory quadrature method is applied to a two-dimensional example. The results based on different versions of new perturbation expansion and the new Green's function deduced from this method are compared to…
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of…
In the context of f(R) theories of gravity, we study the cosmological evolution of scalar perturbations by using a completely general procedure. We find that the exact fourth-order differential equation for the matter density perturbations…
While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian…
We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second and higher order perturbations. We first derive some mathematical results…
We present a new first-principle theory for the calculation of the macroscopic second-order susceptibility chi^(2), based on the Time-Dependent Density-Functional Theory approach. Our method allows to include straightforwardly the many-body…
We study an expansion method for high-dimensional parabolic PDEs which constructs accurate approximate solutions by decomposition into solutions to lower-dimensional PDEs, and which is particularly effective if there are a low number of…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
We investigate the gravitational lens effect caused by a non-spherically distorted compact object. The non-spherical property of the gravitational potential is modeled by a quadrupole moment. Under the assumption that the quadrupole…
The cubic anisotropy model provides a simple example of a system with an arbitrarily weak first-order phase transition. We present an analysis of this model using $\eps$-expansion techniques with results up to next-to-next-to-leading order…
In this work, we base on the second-order post-Minkowskian equations of motion, and apply an iterative technique to analytically derive the gravitational deflection of the relativistic particles in the equatorial plane of Kerr-Newman black…
In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is…