Related papers: Biot-Savart type magnetic field quantization via p…
The Biot-Savart law is a well-known and powerful theoretical tool used to calculate magnetic fields due to currents in magnetostatics. We extend the range of applicability and the formal structure of the Biot-Savart law to electrostatics by…
In the introductory courses on electromagnetism, the Biot-Savart law is generally explained by a simple example to find the magnetic field created at any point in space by a small wire element that carries a current. The simplest system…
The method of retarded potentials is used to derive the Biot-Savart law, taking into account the correction that describes the chaotic motion of charged particles in rectilinear currents. Then this method is used for circular currents and…
Recently, the entanglement dynamics of two harmonic oscillators initially prepared in a separable-coherent state was demonstrated to offer a pathway for prime number identification. This article presents a generalized approach and outlines…
One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot-Savart field from each straight segment is known analytically.…
The purpose of this paper is to derive the on and off-axes magnetic field of a solenoid with the use of a novel method. We have found a solution for the Biot-Savart law by considering the solenoid with a stationary electric current. The…
In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible…
This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed…
Micromagnetics depends on high-fidelity numerical methods for magnetization dynamics. This work proposes a third-order temporal accuracy scheme for the Landau-Lifshitz-Gilbert equation, addressing accuracy-efficiency trade-offs in existing…
A dynamic sieve method is designed according to the basic sieve method. It mainly refers to the symbolic dynamics theory. By this method, we could connect the prime system with familiar 'Logistic Mapping'. An interesting discovery is that…
We implement a quantum protocol for prime number identification based on entanglement dynamics, using IBM quantum processors. The method links the primality of an integer to specific Fourier components extracted from the time evolution of…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
Optimally-shaped electromagnetic fields have the capacity to coherently control the dynamics of quantum systems and thus offer a promising means for controlling molecular transformations relevant to chemical, biological, and materials…
A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling…
We present a theory for the estimation of a classical magnetic field by an atomic sample with a gaussian distribution of collective spin components. By incorporating the magnetic field and the probing laser field as quantum variables with…
This contribution documents the methods used in the BioSaw code. The code is inteded to be a flexible tool for calculating magnetic fields due to coils in magnetic confinement fusion devices. It assumes the conductors are infinitesimally…
To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…
Signal processing has played, and continues to play, a fundamental role in the evolution of modern localization technologies. Localization using spatial variations in the Earth's magnetic field is no exception. It relies on…
The non-invasive spatiotemporal control of cellular functions, organization of tissues, and even the behavior of small animals has become paramount for advanced therapies. As magnetic fields do not interact with biological matter, their…
Number theory is considered, by proposing quantum mechanical models and string-like models at zero and finite temperatures, where the factorization of number into prime numbers is viewed as the decay of particle into elementary particles…