Tao Yang · Ming C Lin · Ralph R Martin · Jian Chang · Shimin Hu. Versatile interactions at interfaces for SPH-based simulations. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation.Page 57-66.2016.
This article presents a novel and flexible bubble modelling technique for multi-fluid simulations using a volume fraction representation. By combining the volume fraction data obtained from a primary multi-fluid simulation with simple and efficient secondary bubble simulation, a range of real-world bubble phenomena are captured with a high degree of physical realism, including large bubble deformation, sub-cell bubble motion, bubble stacking over the liquid surface, bubble volume change, dissolving of bubbles, etc. Without any change in the primary multi-fluid simulator, our bubble modelling approach is applicable to any multi-fluid simulator based on the volume fraction representation.
Finster, Felix. "A variational principle in discrete space–time: existence of minimizers." Calculus of Variations and Partial Differential Equations 29.4 (2007): 431-453.
Finster, Felix. "Fermion systems in discrete space–time—outer symmetries and spontaneous symmetry breaking." Advances in Theoretical and Mathematical Physics 11.1 (2007): 91-146.
Finster, Felix. "On the regularized fermionic projector of the vacuum." Journal of Mathematical Physics 49.3 (2008): 032304.
Deckert, D-A., et al. "Time-evolution of the external field problem in quantum electrodynamics." Journal of Mathematical Physics (2010).
Finster, Felix, Simone Murro, and Christian Röken. "The fermionic projector in a time-dependent external potential: Mass oscillation property and Hadamard states." Journal of Mathematical Physics 57.7 (2016): 072303.
Finster, Felix, and Jürgen Tolksdorf. "Perturbative description of the fermionic projector: Normalization, causality, and Furry's theorem." Journal of Mathematical Physics 55.5 (2014): 052301.
Finster, Felix, and Stefan Hoch. "An action principle for the masses of Dirac particles." Advances in Theoretical and Mathematical Physics 13.6 (2009): 1653-1711.
Finster, Felix. "From discrete space-time to Minkowski space: Basic mechanisms, methods and perspectives." Quantum Field Theory. Birkhäuser Basel, 2009. 235-259.
Bernard, Yann, and Felix Finster. "On the structure of minimizers of causal variational principles in the non-compact and equivariant settings." Advances in Calculus of Variations 7.1 (2014): 27-57.
Diethert, Alexander, Felix Finster, and Daniela Schiefeneder. "FERMION SYSTEMS IN DISCRETE SPACE–TIME EXEMPLIFYING THE SPONTANEOUS GENERATION OF A CAUSAL STRUCTURE." International Journal of Modern Physics A 23.27n28 (2008): 4579-4620.
The ``principle of the fermionic projector'' provides a new mathematical framework for the formulation of physical theories and is a promising approach for physics beyond the standard model. The book begins with a brief review of relativity, relativistic quantum mechanics and classical gauge theories, with the emphasis on the basic physical concepts and the mathematical foundations. The external field problem and Klein's paradox are discussed and then resolved by introducing the so-called fermionic projector, a global object in space-time which generalizes the notion of the Dirac sea. The mathematical core of the book is to give a precise definition of the fermionic projector and to employ methods of hyperbolic differential equations for its detailed analysis. The fermionic projector makes it possible to formulate a new type of variational principles in space-time. The mathematical tools for the analysis of the corresponding Euler-Lagrange equations are developed. A particular variational principle is proposed which gives rise to an effective interaction showing many similarities to the interactions of
the standard model.
The main chapters of the book are easily accessible for beginning graduate students in mathematics or physics. Several appendices provide supplementary material which will be useful to the experienced researcher.
Tiexiang LiDepartment of Mathematics, Southeast UniversityTsung-Ming HuangDepartment of Mathematics, National Taiwan Normal UniversityWen-Wei LinDepartment of Applied Mathematics, National Chiao Tung UniversityJenn-Nan WangInstitute of Applied Mathematics, National Taiwan University
We study a robust and efficient eigensolver for computing the positive dense spectrum of the two-dimensional transmission eigenvalue problem (TEP) which is derived from the Maxwell’s equation with complex media in pseudo-chiral model and the transverse magnetic mode. The discretized governing equations by the N ́ed ́elec edge element result in a large-scale quadratic eigenvalue problem (QEP). We estimate half of the positive eigenvalues of the QEP are on some interval which forms a dense spectrum of the QEP. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Intensive numerical experiments show that our proposed method makes the convergence efficiently and robustly even it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by the non- linear functions which can be applied to estimate the density of the eigenvalues for the TEP.
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two possible modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system.
In the second model the resulting equation is a wave equation in $\so \times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions for each fixed $\xi$. This set of equations contains as a special case the equation of a quantized cosmological Friedman universe without matter but with a cosmological constant, when we look for solutions which only depend on $t$. Moreover, in case $\so$ is compact we prove a spectral resolution of the equation.
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse problems of recovering continuous (infinite dimensional) coefficient functions from ordinary or partial differential equations, a problem which is typically ill-posed. Regularization of these problems using L2 function spaces (Tikhonov regularization) is equivalent to Bayesian probabilistic inference, using a Gaussian prior. The Bayesian interpretation of inverse problem regularization is useful since it allows one to quantify and characterize error and degree of precision in the solution of inverse problems, as well as examine assumptions made in solving the problem—namely whether the subjective choice of regularization is compatible with prior knowledge. Using path-integral formalism, Bayesian inference can be explored through various perturbative techniques, such as the semiclassical approximation, which we use in this manuscript. Perturbative path-integral approaches, while offering alternatives to computational approaches like Markov-Chain-Monte-Carlo (MCMC), also provide natural starting points for MCMC methods that can be used to refine approximations. In this manuscript, we illustrate a path-integral formulation for inverse problems and demonstrate it on an inverse problem in membrane biophysics as well as inverse problems in potential theories involving the Poisson equation.