arXiv subjects

Daiju Nakayama

Publications and source records attributed to Daiju Nakayama.

4 recordsLinked to original sources

arXiv2025

Seeing through the light cone: Visualizing electromagnetic fields in special relativity

The theoretical framework of electromagnetism played a foundational role in Einstein's development of special relativity. To support conceptual understanding, we present a fully special relativistic computer simulation that visualizes electromagnetic fields from the perspective of a moving observer. In this simulation, the user observes electromagnetic phenomena through their past light cone and directly experiences the Lorentz force acting at that spacetime point. The electromagnetic field is computed from the subluminal motion of point charges at the intersection of their worldlines with the observer's past light cone, ensuring causal consistency and Lorentz covariance. This approach offers an interactive and intuitive representation of relativistic electromagnetism. It provides insight into how electric and magnetic fields transform across inertial frames, and serves as a bridge between abstract formalism and physical intuition. The simulation also lends itself to pedagogical use in courses on special relativity or electrodynamics.

physics.ed-ph↗

arXiv2025

Covariant Electromagnetism in Past-Light-Cone Formalism

We present a manifestly covariant formulation of relativistic electromagnetism, focusing on the computation of electromagnetic fields from moving charges in a manifestly Lorentz-covariant manner. The electromagnetic field at a given spacetime point is determined by the motion of point charges at the intersection of their worldlines with the past light cone of the spacetime point, ensuring causal consistency. This formalism provides a manifestly covariant generalization of the Liénard-Wiechert potentials and allows direct implementation on computers. We compare our formulation with standard textbook approaches and analyze its behavior in various physical limits.

physics.class-ph↗

arXiv2017

Relativity for games

We present how to implement special relativity in computer games. The resultant relativistic world shows the time dilation and Lorentz contraction exactly, not only for the player but also for all the nonplayer characters, who obey the correct relativistic equation of motion according to their own accelerations. Causality is explicitly maintained in our formulation by use of the covariant velocities, proper times, worldlines, and light cones. Faraway relativistic scenes can be accurately projected onto the skydome. We show how to approximate a rigid body consisting of polygons, which is ubiquitous in computer games but itself is not a relativistically invariant object. We also give a simple idea to mimic the Doppler effect within the RGB color scheme.

physics.class-ph↗

arXiv2016

Protocol-dependent shear modulus of amorphous solids

We investigate the linear elastic response of amorphous solids to a shear strain at zero temperature. We find that the response is characterized by at least two distinct shear moduli. The first one, $μ_{\rm ZFC}$, is associated with the linear response of a single energy minimum. The second, $μ_{\rm FC}$, is related to sampling, through plastic events, an ensemble of distinct energy minima. We provide examples of protocols that allow one to measure both shear moduli. In agreement with a theoretical prediction based on the exact solution in infinite spatial dimensions, the ratio $μ_{\rm FC}/μ_{\rm ZFC}$ is found to vanish proportionally to the square root of pressure at the jamming transition. Our results establish that amorphous solids are characterized by a rugged energy landscape, on which the infinite-dimensional solution can give useful insight.

cond-mat.soft↗