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General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order Godunov-type schemes. In the past, building a generalized Riemann problem solver was seen as…
The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in terms of the structure and in terms of the spectral features of…
Based on Regge-inspired arguments and counting rules, we formulate empirical models for zero-skewness generalized parton distributions (GPDs) ${\widetilde H}^{(3)}$ and ${\widetilde E}^{(3)}$ in the iso-vector sector. If a hypothetical…
In the era of 2D and quasi-2D quantum materials one needs to model strain at the level of the Hamiltonian as opposed to a semi-classical approach. Corrections to the electronic Hamiltonian due to strain arise from two sources: deformations…
We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor (NN) and…
In this paper, we demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coefficients. The optimal coarse basis can be derived automatically…
We formulate and implement a spectral method for solving the Schrodinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials…
Generalized parton distributions (GPDs) are key quantities for the description of a hadron's three-dimensional structure. They are the current focus of all areas of hadronic physics -- phenomenological, experimental, and theoretical,…
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a robust parallel domain decomposition preconditioner for…
One-dimensional integrable and quasi-integrable systems display, on macroscopic scales, a universal form of transport known as Generalized Hydrodynamics (GHD). In its standard Euler-scale formulation, GHD mirrors the equations of a…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
Generalized Parton Distributions (GPDs) have emerged as a powerful framework for exploring the internal structure of hadrons in terms of their partonic constituents. Over the past three decades, the field has witnessed significant…
To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
The generalised balanced power diagram (GBPD) is regarded in the literature as a suitable geometric model for describing polycrystalline microstructures with curved grain boundaries. This article compiles properties of GBPDs with regard to…
Many problems in Euclidean geometry, arising in computational design and fabrication, amount to a system of constraints, which is challenging to solve. We suggest a new general approach to the solution, which is to start with analogous…
The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light…