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A very general saddle point nuclear shape may be found as a solution of an integro-differential equation without giving apriori any shape parametrization. By introducing phenomenological shell corrections one obtains minima of deformation…
We compute and explore numerically the finite system size correction to NLO $2\to2$ scattering in massive scalar $\phi^4$ theory. The derivation uses "denominator regularization" (instead of the usual dimensional regularization) on a…
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
I briefly present recent work on QCD power corrections in heavy-to-light meson decays, using an effective field theory approach.
The Perdew-Zunger(PZ) self-interaction correction (SIC) was designed to correct the one-electron limit of any approximate density functional for the exchange-correlation (xc) energy, while yielding no correction to the exact functional.…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
The present article describes the size induced changes in the structural arrangement of intrinsic defects present in chemically synthesized ZnO nanoparticles of various sizes. Routine X-ray diffraction (XRD) and Transmission Electron…
All-solid-state batteries are seen as promising candidates to replace conventional batteries with liquid electrolytes in many applications. However, they are not yet feasible for many relevant applications. One particular question of…
Bertaut's equivalent electric density idea (E. F. Bertaut, Journal de Physique {\bf 39}, 1331 (1978)) is applied to the case of two dimensional periodic continuous charge density distributions. The following derivation differs from what was…
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The M-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…
The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves…
The article considers a new mechanism of charge accumulation in the early Universe in theories with compact extra dimensions. The relaxation processes in the extra space metric that take place during its formation lead to the establishment…
We consider (a) the partition functions of the anisotropic dimer model on the rectangular (2M-1) x (2N-1) lattice with free and cylindrical boundary conditions with a single monomer residing on the boundary and (b) the partition function of…
In this article, we study the speed of convergence of the supercell reduced Hartree-Fock~(rHF) model towards the whole space rHF model in the case where the crystal contains a local defect. We prove that, when the defect is charged, the…
In order to optimize the optoelectronic properties of novel solar cell architectures, such as the amorphous-crystalline interface in silicon heterojunction devices, we calculate and analyze the local microscopic structure at this interface…
The development of high-energy and high-power density supercapacitors (SCs) is critical for enabling next-generation energy storage applications. Nanocarbons are excellent SC electrode materials due to their economic viability, high-surface…