Related papers: An algorithm for coalescence of classical objects …
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The empirical formula proposed by J. D. Anderson et al. [1] to reproduce the data on the Earth flyby anomalies is derived from special relativity (SR). The transverse Doppler shift together with the addition of velocities account for the…
In the first part of a series of two papers, we present in considerable detail a collision-driven molecular dynamics algorithm for a system of nonspherical particles, within a parallelepiped simulation domain, under both periodic or…
Self-propelled colloidal swimmers move by pushing the adjacent fluid backwards. The resulting motion of an asymmetric body depends on the profile of pushing velocity over its surface. We describe a method of predicting the motion arising…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
The nature takes the easiest and most accessible paths and, hence, processes are accomplished very quickly in a minimum time. In 1662 P. Fermat used this principle to work out the refraction law. This was one of the first known attempts at…
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous…
In the fields of statistics and unsupervised machine learning a fundamental and well-studied problem is anomaly detection. Anomalies are difficult to define, yet many algorithms have been proposed. Underlying the approaches is the nebulous…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…
We consider the $N$-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of locked inertia tensor, we compute the moment of inertia for systems moving on spheres and hyperbolic spheres and show that…
Automatic detection of visual anomalies and changes in the environment has been a topic of recurrent attention in the fields of machine learning and computer vision over the past decades. A visual anomaly or change detection algorithm…
Several algorithms in computer algebra involve the computation of a power series solution of a given ordinary differential equation. Over finite fields, the problem is often lifted in an approximate $p$-adic setting to be well-posed. This…
Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic light-corpuscle arguments. However, Newton was also a proponent of wave/particle duality, and published a "new" variable-density aether model in…
In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz…
We present an explicit multiscale algorithm for solving differential equations for problems with high-frequency modes that can be averaged over by separating and scaling the fast and slow dynamics within a single equation. We introduce a…
The Lorentz equations describe the motion of electrically charged particles in electric and magnetic fields and are used widely in plasma physics. The most popular numerical algorithm for solving them is the Boris method, a variant of the…