相关论文: Hyperbolic formulations and numerical relativity: …

This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal…

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…

Many traditional algorithms applied in gravitational-wave astronomy rely on the assumption of Gaussian noise, a condition not always met. To meet this need, this study extends a robust statistical framework, advancing previous work on…

This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…

We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the…

We show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some essential results…

When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…

This paper investigates the possible use of the Hyperspherical Adiabatic basis in the description of scattering states of a three-body system. In particular, we analyze a 1+2 collision process below the three-body breakup. The convergence…

Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…

In this article we provide an integration formula making us able to integrate random variables defined on the moduli space of hyperbolic surfaces which involve the lengths of closed geodesics belonging to a fixed arbitrary mapping class…

We consider a chain of $n$ coupled oscillators placed on a one-dimensional lattice with periodic boundary conditions. The interaction between particles is determined by a weakly anharmonic potential $V_n = r^2/2 + \sigma_nU(r)$, where $U$…

A new computationally efficient method has been introduced to treat self-gravity in mesh based hydrodynamical simulations. It is applied simply by slightly modifying the Poisson equation into an inhomogeneous wave equation. This roughly…

It is well known that for solutions of semi-linear parabolic PDEs, there are equivalent probabilistic interpretations, which yields the so called nonlinear Feymman-Kac formula. By adopting such formula, we consider in this work a novel…

This paper investigates the zero relaxation limit for general linear hyperbolic relaxation systems and establishes the asymptotic convergence of slow variables under the unimprovable weakest stability condition, akin to the Lax equivalence…

We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice…

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…

We develop a method for studying the real time dynamics of Heisenberg operators in strongly-interacting nonequilibrium quantum impurity models. Our method is applicable to a wide range of interaction strengths and to bias voltages beyond…

We develop a time-dependent variational Monte Carlo (t-VMC) method for quantum dynamics of strongly correlated electrons. The t-VMC method has been recently applied to bosonic systems and quantum spin systems. Here, we propose a…

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…