相关论文: Implementing Few-Body Algorithmic Regularization w…

We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly…

This study presents a novel optimisation technique for atomic structure calculations using the Flexible Atomic Code, focussing on complex multielectron systems relevant to $r$-process nucleosynthesis and kilonova modelling. We introduce a…

We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the…

We introduce a method for global optimization of the structure of atomic systems that uses additional atoms with fractional existence. The method allows for movement of atoms over long distances bypassing energy barriers encountered in the…

We study the spherical collapse in the Parametrized Post-Friedmannian (PPF) scheme. We use a general form of the PPF parameter related to the Poisson equation and found the equations to solve that includes a non-trivial fifth force coming…

The post-Newtonian gravitoelectric secular rate of the mean anomaly M is worked out for a two-body system in the framework of the General Theory of Relativity. The possibility of using such an effect, which is different from the well known…

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…

In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite element discretization of linear or nonlinear inverse…

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an astronomical N-body system. To do this, we generalize…

For $n$-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the…

Szemer\'edi's regularity lemma and its variants are some of the most powerful tools in combinatorics. In this paper, we establish several results around the regularity lemma. First, we prove that whether or not we include the condition that…

The asymptotic nature of unbound binary-black-hole encounters provides a clean method for comparing different approaches for modeling the two-body problem in general relativity. In this work, we use numerical relativity simulations of…

Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is…

We develop a renormalisation scheme for time--ordered products in interacting field theories on curved spacetimes which consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This…

We provide a methodology for decoupling the bulk gravitational field equations of braneworld black holes to suppress the bulk singularities. Thus, we provide a regular braneworld black hole setup. To achieve this, we apply a Minimal…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

Effective-one-body (EOB) waveforms employed by the LIGO-Virgo-KAGRA Collaboration have primarily been developed by resumming the post-Newtonian expansion of the relativistic two-body problem. Given the recent significant advancements in…

We construct quasiequilibrium sequences of black hole-neutron star binaries in general relativity. We solve Einstein's constraint equations in the conformal thin-sandwich formalism, subject to black hole boundary conditions imposed on the…