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A new spectral code for constructing general-relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
We describe an approach to numerical simulation of spiral waves dynamics of large spatial extent, using small computational grids.
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
The purpose of this article is to introduce the reader to the ROOT data analysis software package, and demonstrate how it may be used to complement one's accident reconstruction analyses.
Assuming a suitable rotation of the Universe as a whole, we can attribute the rotation of galaxies to it. Using Lagrangian Mechanics we then can find the equations governing the rotation of a galaxy. We find in this way the azimuthal…
The availability of computational modeling tools for subatomic physics (Form, FeynArts, FormCalc, and FeynCalc) has made it possible to perform sophisticated calculations in perturbative quantum field theory. We have adapted these packages…
This is a set of lecture notes used in a graduate topic class in applied mathematics called ``Quantum Algorithms for Scientific Computation'' at the Department of Mathematics, UC Berkeley during the fall semester of 2021. These lecture…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
In this thesis, we introduce novel methods for analyzing pulsar populations using a variety of mathematical techniques. These tools-particularly graph theory-have been thoroughly validated in advanced mathematics, enabling us to overcome…
The study of thrombosis is crucial to understand and develop new therapies for diseases like deep vein thrombosis, diabetes related strokes, pulmonary embolism etc. The last two decades have seen an exponential growth in studies related to…
We present a web-based application designed to simulate rotational light curves of small airless Solar System bodies under user-defined geometrical and physical conditions. The tool integrates both physical and empirical photometric models…
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
Convenient and simple numerical techniques for performing quantum computations based on matrix representations of Hilbert space operators are presented and illustrated by various examples. The applications include the calculations of…
We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…
Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…
A set of MapleV R.4/5 software routines for calculating the numerical evolution of dynamical systems and flexibly plotting the results is presented. The package consists of an initial condition generator (on which the user can impose quite…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
Understanding the morphology of galaxies is a critical aspect of astrophysics research, providing insight into the formation, evolution, and physical properties of these vast cosmic structures. Various observational and computational…
The classification of galaxies as spirals or ellipticals is a crucial task in understanding their formation and evolution. With the arrival of large-scale astronomical surveys, such as the Sloan Digital Sky Survey (SDSS), astronomers now…