Related papers: On Third-Order Limiter Functions for Finite Volume…
When dealing with stiff conservation laws, explicit time integration forces to employ very small time steps, due to the restrictive CFL stability condition. Implicit methods offer an alternative, yielding the possibility to choose the time…
We propose inverse renormalization group transformations to construct approximate configurations for lattice volumes that have not yet been accessed by supercomputers or large-scale simulations in the study of spin glasses. Specifically,…
We reconsider the ellipsoid method for linear inequalities. Using the ellipsoid representation of Burrell and Todd, we show the method can be viewed as coordinate descent on the volume of an enclosing ellipsoid, or on a potential function,…
We discuss a classical mistake, made in earlier publications on the stick percolation problem in 3D, for generating the right isotropic configuration of sticks. We explain the observed systematic deviations from the excluded volume rule.…
We study the restricted volume of effective divisors, its properties and the relationship with the related notion of reduced volume, defined via multiplier ideals, and with the asymptotic intersection number. We build upon the fundamental…
The optimization of shape functionals under convexity, diameter or constant width constraints shows numerical challenges. The support function can be used in order to approximate solutions to such problems by finite dimensional optimization…
This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $\mu$-strongly convex. We show that no algorithm can reach an error $\epsilon$ in minimizing all functions from…
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order H\"older smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are H\"older continuous with…
We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when…
An incremental-stencil WENO reconstruction method, which uses low-order candidate stencils with incrementally increasing width, is proposed for finite-volume simulation of compressible two-phase flow with the quasi-conservative interface…
We calculate universal finite size scaling functions for the order parameter and the longitudinal susceptibility of the three-dimensional O(4) model. The phase transition of this model is supposed to be in the same universality class as the…
A complete family of functional Steiner formulas is established. As applications, an explicit representation of functional intrinsic volumes using special mixed Monge-Amp\`ere measures and a new version of the Hadwiger theorem on convex…
The finite volume correction for a mean-field monomer-dimer system with an attractive interaction are computed for the pressure density, the monomer density and the susceptibility. The results are obtained by introducing a two-dimensional…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
The perturbative result for the quark-mass conversion factor between the $\overline{\mathrm{MS}}$ and regularization-independent symmetric-momentum subtraction scheme (RI/SMOM) away from the chiral limit, i.e. at non-zero quark masses…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an…
The three-dimensional reconstruction of vocal folds in medicine usually involves endoscopy and an approach to extract depth information like structured light or stereo matching of images. The resulting mesh can accurately represent the…
In this paper, a compact third-order gas-kinetic scheme is proposed for the compressible Euler and Navier-Stokes equations. The main reason for the feasibility to develop such a high-order scheme with compact stencil, which involves only…
We define a volume function on configurations of four points in the 3-sphere which is invariant under the action of PU(2,1), the automorphism group of the CR structure defined on the sphere by its embedding in complex 2-space. We show that…