Article
Astronomy & Astrophysics
Jan Ambjorn, Zbigniew Drogosz, Jakub Gizbert-Studnicki, Andrzej Gorlich, Jerzy Jurkiewicz, Daniel Nemeth
Summary: This article discusses the complex geometries extracted from the path integral of a quantum theory of gravity, showing that using suitable coordinate systems and scalar fields that solve Laplace's equation can help understand cosmic voids and filaments structures. It also demonstrates the dramatic changes in geometry that can occur when scalar fields are dynamically coupled to the geometry.
CLASSICAL AND QUANTUM GRAVITY
(2021)
Article
Mathematics, Applied
Colette Anne, Hela Ayadi, Yassin Chebbi, Nabila Torki-Hamza
Summary: This paper extends the notions of magnetic difference operator and magnetic exterior derivative to 2-simplicial complexes called triangulations, in a manner compatible with gauge transformations. It then studies the magnetic Gauss-Bonnet operator defined in this context and introduces the geometric hypothesis of chi-completeness, which ensures the essential self-adjointness of this operator. This also provides the essential self-adjointness of the magnetic Laplacian on triangulations. Finally, it introduces the hypothesis of bounded curvature for the magnetic potential to characterize the domain of the self-adjoint extension.
Article
Physics, Particles & Fields
Siddharth Tiwary, Rainer Dick
Summary: Antisymmetric tensor fields, predicted by string theory, offer an interesting target for particle physics due to their potential coupling to electromagnetic dipole moments. The strongest constraints on electromagnetic dipole couplings come from couplings to electrons, with previous measurements of Bhabha scattering setting limits on these interactions.
EUROPEAN PHYSICAL JOURNAL C
(2021)
Article
Mathematics
Vladimir Turaev
Summary: The topology of a space can give rise to tensor fields on the moduli spaces of the fundamental group.
ADVANCES IN MATHEMATICS
(2021)
Article
Physics, Particles & Fields
Alessandro Candido, Giuseppe Clemente, Massimo D'Elia, Federico Rottoli
Summary: This study focuses on the discretization of Yang-Mills theories on Dynamical Triangulations and the numerical investigation of the minimally coupled system. Results include explicit construction and implementation of Markov chain moves, as well as exploratory numerical simulations on toroidal geometry. Critical behavior of gravity-related observables and gauge observables are studied, with interesting findings on the suppression of critical slowing down in the presence of locally variable geometry.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Astronomy & Astrophysics
H. Khodabakhshi, H. Lu, R. B. Mann
Summary: The gravitational Lagrangian can be decomposed into a bulk term and a total derivative term. In certain theories of gravity like Einstein or Lovelock gravities, there are holographic relations between the bulk and the total derivative term, where the latter is determined by the former. However, at the D -> 2 and D -> 4 limits, the bulk terms of Einstein or Gauss-Bonnet theories become total derivatives themselves. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities leads to two-dimensional or four-dimensional scalar-tensor theories respectively. We derived holographic relations for the D = 2 and D = 4 cases, which have the same form as the holographic relations in pure gravity in the foliation independent formalism.
Article
Astronomy & Astrophysics
Hector O. Silva, Andrew Coates, Fethi M. Ramazano, Thomas P. Sotiriou
Summary: Spontaneous scalarization allows scalar fields to go undetected in weak gravity and develop nontrivial configurations in strong gravity. However, generalizing this mechanism to vector fields faces a serious obstacle as a ghost appears.
Article
Astronomy & Astrophysics
G. Yu. Prokhorov, O. V. Teryaev, V. I. Zakharov
Summary: The article calculates the gravitational chiral quantum anomaly in the extended RaritaSchwinger-Adler (RSA) field theory framework, which includes the interaction with an additional spin 1/2 field. It is found that the factor in the gravitational chiral anomaly normalized to the Dirac field anomaly is equal to -19, distinguishing the RSA theory from other theories of spin 3/2. The conformality of the RSA theory is directly verified through one-loop three-point graphs in the strong interaction limit.
Article
Mathematics, Applied
Alexander Effland, Behrend Heeren, Martin Rumpf, Benedikt Wirth
Summary: The study successfully approximates the Riemann curvature tensor and sectional curvatures by extending the variational time discretization of geodesic calculus. Experimental validation confirms the effectiveness of the method in practical applications and provides a basis for further research.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
David Glickenstein
Summary: This paper uses weighted triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. A geometric structure on the Poincare dual is constructed by considering weights at the vertices. The properties of these geometric structures and how to find nondegenerate weighted triangulations are studied. The possibilities of discrete Riemannian manifolds are briefly discussed.
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
(2024)
Article
Astronomy & Astrophysics
Abhay Ashtekar, Adrian del Rio
Summary: Recent studies have shown that linear quantum fields can be propagated across renormalized observables in Minkowskian quantum field theories. They can also be extended as well-defined distributions even in spacetimes that include the big bang or the big crunch. This generalization has been applied to spatially closed and open FLRW models, demonstrating that the tameness of cosmological singularities is not dependent on spatial flatness.
Article
Mathematics, Applied
Xiaoyu Song, Baodong Zheng, Riguang Huang
Summary: This paper completely characterizes the maximum rank of m x n x 2 tensors over an arbitrary field. The maximal tensor rank may differ over different fields, but the maximum rank of a given m x n x 2 tensor is consistent over any field except F-2.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
O. Diatlyk
Summary: This study extends classic results about the energy-momentum tensor near an evaporating black hole by considering a massive scalar field in a two-dimensional space with a thin shell collapse. The research shows that the WKB approximation is valid outside the shell when mr(g) >>1, and the radiation near the shell and at spatial infinity exhibits thermal characteristics with Hawking temperature. The negative flux T-vv near the shell is similar to the classic result in the massless case.
Article
Mathematics, Applied
Shuo Zhang
Summary: This paper introduces a nonconforming finite element scheme for the planar biharmonic equation, which achieves O(h(2)) convergence rate for smooth solutions on general shape-regular triangulations. The scheme is based on a piecewise cubic polynomial space that can approximate H-4 functions with O(h(2)) accuracy in the broken H-2 norm.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yuan Zhao, Guoyan Zhao, Jing Zhou, Ju Ma, Xin Cai
Summary: The combination of acoustic emission and moment tensor simulation is effective in analyzing rock failure mechanisms, with critical values for distinguishing implosion, shear, and tensile mechanisms identified and shown to be more accurate than counting microcracks for identifying rock failure mechanisms. Quantitative determination of macrocrack fracture mechanisms can be achieved through the distribution curve of AE events.
COMPUTERS AND GEOTECHNICS
(2021)
Article
Mathematics, Applied
Melissa Yeung, David Cohen-Steiner, Mathieu Desbrun
Article
Computer Science, Software Engineering
Max Budninskiy, Ameera Abdelaziz, Yiying Tong, Mathieu Desbrun
COMPUTER AIDED GEOMETRIC DESIGN
(2020)
Article
Computer Science, Software Engineering
Wei Li, Yixin Chen, Mathieu Desbrun, Changxi Zheng, Xiaopei Liu
ACM TRANSACTIONS ON GRAPHICS
(2020)
Article
Computer Science, Software Engineering
Lois Paulin, Nicolas Bonneel, David Coeurjolly, Jean-Claude Iehl, Antoine Webanck, Mathieu Desbrun, Victor Ostromoukhov
ACM TRANSACTIONS ON GRAPHICS
(2020)
Article
Computer Science, Software Engineering
Fernando de Goes, Andrew Butts, Mathieu Desbrun
ACM TRANSACTIONS ON GRAPHICS
(2020)
Article
Computer Science, Software Engineering
Kai Bai, Wei Li, Mathieu Desbrun, Xiaopei Liu
Summary: The article proposes a novel learning approach for dynamically upsampling smoke flows based on a training set of coarse and fine resolution flows. The network constructs a corresponding dictionary during training and is able to provide accurate upsampling through fast evaluation.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Jiong Chen, Florian Schaefer, Jin Huang, Mathieu Desbrun
Summary: The article introduces an efficient preconditioning method for large-scale and ill-conditioned sparse linear systems, using techniques such as incomplete Cholesky factorization, fine-to-coarse ordering, multiscale sparsity pattern, and conjugate gradient solver. This approach outperforms existing carefully-engineered libraries for graphics problems involving bad mesh elements and/or high contrast of coefficients. The core concepts are supported by theoretical foundations, linking operator-adapted wavelets to Cholesky factorization and multiscale analysis.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Wei Li, Daoming Liu, Mathieu Desbrun, Jin Huang, Xiaopei Liu
Summary: This article proposes a kinetic model coupling the Navier-Stokes equations with a conservative phase-field equation to provide a general multiphase flow solver. The resulting algorithm is embarrassingly parallel, conservative, far more stable than current solvers, and general enough to capture typical multiphase flow behaviors.
IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Kai Bai, Chunhao Wang, Mathieu Desbrun, Xiaopei Liu
Summary: This paper presents a simple and effective method for spatio-temporal upsampling of fluid simulation using a dictionary-based approach. The neural network approach can accurately reproduce the visual complexity of turbulent flows from coarse velocity fields, demonstrating efficiency and generalizability for predicting high-resolution turbulence details.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Chaoyang Lyu, Wei Li, Mathieu Desbrun, Xiaopei Liu
Summary: This paper proposes an efficient and versatile approach for simulating two-way fluid-solid coupling in the kinetic fluid simulation framework, addressing the challenges of reproducing the interaction between fluids and solids. The novel hybrid approach introduced in the paper ensures a robust and plausible treatment of turbulent flows near moving solids, significantly reducing boundary artifacts. Simple GPU optimizations are also presented to achieve a higher computational efficiency than existing methods.
ACM TRANSACTIONS ON GRAPHICS
(2021)
Article
Computer Science, Software Engineering
Wei Li, Yihui Ma, Xiaopei Liu, Mathieu Desbrun
Summary: This paper proposes a new solver for coupling the incompressible Navier-Stokes equations with a conservative phase-field equation to simulate multiphase flows. The resulting solver shows efficiency, versatility, and reliability in dealing with large density ratios, high Reynolds numbers, and complex solid boundaries.
ACM TRANSACTIONS ON GRAPHICS
(2022)
Article
Computer Science, Software Engineering
Jiayi Wei, Jiong Chen, Damien Rohmer, Pooran Memari, Mathieu Desbrun
Summary: This paper presents a new robust-statistics approach for denoising pointsets, preserving sharp features by using line processes and offering robustness to noise and outliers. Our method deduces a geometric denoising strategy through robust and regularized tangent plane fitting, obtained numerically for efficiency and reliability. We use line processes to identify inliers vs. outliers and to detect the presence of sharp features.
COMPUTER GRAPHICS FORUM
(2023)
Article
Computer Science, Software Engineering
Wei Li, Mathieu Desbrun
Summary: This paper presents an improved numerical simulation method that can accurately simulate complex fluid phenomena and effectively handle fluid-solid coupling. It introduces a series of numerical improvements in momentum exchange, interfacial forces, and two-way coupling to reduce simulation artifacts and expand the types of fluid-solid coupling that can be efficiently simulated. The benefits of the solver are demonstrated through challenging simulation results and comparisons to previous work and real footage.
ACM TRANSACTIONS ON GRAPHICS
(2023)
Article
Mathematics, Applied
Rui Wang, Rundong Zhao, Emily Ribando-Gros, Jiahui Chen, Yiying Tong, Guo-Wei Wei
Summary: The introduction of persistent spectral graph theory expands the multi-scale paradigm of topological data analysis and geometric analysis. The harmonic spectra constructed from the persistent Laplacian matrices provide topological invariants such as persistent Betti numbers, while the non-harmonic spectra offer additional geometric analysis of the data shape.
FOUNDATIONS OF DATA SCIENCE
(2021)
Article
Mathematics, Applied
Jiahui Chen, Rundong Zhao, Yiying Tong, Guo-Wei Wei
Summary: The evolutionary de Rham-Hodge method proposed in this work provides a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds, with a focus on compact manifolds with 2-manifold boundaries. The proposed method introduces three sets of unique evolutionary Hodge Laplacians to generate topology-preserving singular spectra, revealing topological persistence and geometric progression during manifold evolution. Extensive numerical experiments validate the potential of the paradigm for data representation and shape analysis, particularly in challenging cases such as protein B-factor predictions where existing biophysical models fail.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)