相关论文: $\varphi$enics: Vainshtein screening with the fini…
In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…
Viable modifications of gravity that may produce cosmic acceleration need to be screened in high-density regions such as the Solar System, where general relativity is well tested. Screening mechanisms also prevent strong anomalies in the…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
In scalar-tensor theories beyond Horndeski, the Vainshtein screening mechanism is only partially effective inside astrophysical bodies. We investigate the potential to detect this partial breaking of Vainshtein screening through the tidal…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
In the first part of this paper we critically examine the ultra-violet implications of theories that exhibit Vainshtein screening, taking into account both the standard Wilsonian perspective as well as more exotic possibilities. Aspects of…
New light scalar degrees of freedom may alleviate the dark matter and dark energy problems, but if coupled to matter, they generally mediate a fifth force. In order for this fifth force to be consistent with existing constraints, it must be…
We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…
We introduce and demonstrate the power of a method to speed up current iterative techniques for N-body modified gravity simulations. Our method is based on the observation that the accuracy of the final result is not compromised if the…
In industry, shape optimization problems are of utter importance when designing structures such as aircraft, automobiles and turbines. For many of these applications, the structure changes over time, with a prescribed or non-prescribed…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
There has been a lot of research interest in modified gravity theories which utilise the Vainshtein mechanism to recover standard general relativity in regions with high matter density, such as the Dvali-Gabadadze-Porrati and Galileon…
Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their…
Observational evidence implying the accelerated expansion of the universe has been the motivation to develop various classes of modified gravity theories. One of them uses the so-called "screening mechanism", which is successful in…
We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem…
In general, modified gravity theories are modifications or extensions of Einstein's general relativity. Some of them give rise to additional scalar degrees of freedom in Nature. If these scalar fields exist and are light enough, they should…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
The Galileon scalar field theory is a prototypical example of an effective field theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity. The Galileon describes the helicity…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…