Related papers: A Primordial Particle System in three dimensions
A multidimensional version of the Yamada-Watanabe theorem is proved. It implies a spectral matrix Yamada-Watanabe theorem. It is also applied to particle systems of squared Bessel processes, corresponding to matrix analogues of squared…
We study a supposed model for branched polymers which was shown in two dimensions to be in the universality class of ordinary percolation. We confirm this by high statistics simulations and show that it is in the percolation universality…
We present the first three-dimensional theoretical model of microparticle-assisted super-resolution imaging, enabling accurate simulation of virtual image formation. The model reveals that accounting for partial spatial coherence of…
Three-dimensional random electron systems undergo quantum phase transitions and show rich phase diagrams. Examples of the phases are the band gap insulator, Anderson insulator, strong and weak topological insulators, Weyl semimetal, and…
A mathematical model of the distribution function for the discrete 3-disk is proposed in order to utilize in the statistical evolution equation of the 3-dimensional Universe. The model distribution is constructed based on analyses in known…
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this…
After an overview of general aspects of modelling the pulsation- convection interaction we present reasons why such simulations (in multidimensions) are needed but, at the same time, pose a considerable challenge. We then discuss, for…
Parallel computing has turned out to be the enabling technology to solve complex physical systems. However, the transition from shared memory, vector computers to massively parallel, distributed memory systems and, recently, to hybrid…
Image matching is still challenging in such scenes with large viewpoints or illumination changes or with low textures. In this paper, we propose a Transformer-based pseudo 3D image matching method. It upgrades the 2D features extracted from…
The implementation of a new particle module describing the physics of dust grains coupled to the gas via drag forces is the subject of this work. The proposed particle-gas hybrid scheme has been designed to work in Cartesian as well as in…
We propose a three-dimensional (3D) multimodal medical imaging system that combines freehand ultrasound and structured light 3D reconstruction in a single coordinate system without requiring registration. To the best of our knowledge, these…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
Systems of particles in a confining potential exhibit a spatially dependent density which fundamentally alters the nature of phase transitions that occur. A specific instance of this situation, which is being extensively explored currently,…
This work continues a series of papers where we propose an algorithm for quasioptical modeling of electromagnetic beams with and without mode conversion. The general theory was reported in the first paper of this series, where a parabolic…
We theoretically study a nanospaser system, which consists of a spherical silver nanoparticle embedded inside a sphere composed of dye molecules. The gain of the system, dye molecules, are described by a three-level model, where the…
As an extension of the former study on 2-dimensional systems, we simulate phase behavior of polymer-grafted colloidal particles in 3 dimensions by molecular Monte Carlo technique in the canonical ensemble. We use a spherically symmetric…
In nature the three-dimensional structure of a protein is encoded in the corresponding gene. In this paper we describe a new method for encoding the three-dimensional structure of a protein into a binary sequence. The feature of the method…
The purpose of this note is to discuss examples of geometric transition from hyperbolic structures to half-pipe and Anti-de Sitter structures in dimensions two, three and four. As a warm-up, explicit examples of transition to Euclidean and…
Superintegrable Hamiltonian systems describing the interactions among three point masses on a line have been described in [2]. Here, we show examples of how the approach of above can be extended to a higher number of particles on a line and…
Applications of the three-dimensional transformation for rotating coordinate systems to quantum mechanics, general theory relativity and optics are considered.