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The vibration of the rails is a significant source of railway rolling noise, often forming the dominant component of noise in the important frequency region between 400 and 2000 Hz. The purpose of the paper is to investigate the influence of the ground profile and the presence of the train body on the sound radiation from the rail.

Two-dimensional boundary element calculations are used, in which the rail vibration is the source. The ground profile and various different shapes of train body are introduced in the model, and results are observed in terms of sound power and sound pressure. Comparisons are also made with vibro-acoustic measurements performed with and without a train present.

The sound radiated by the rail in the absence of the train body is strongly attenuated by shielding due to the ballast shoulder. When the train body is present, the sound from the vertical rail motion is reflected back down toward the track where it is partly absorbed by the ballast. Nevertheless, the sound pressure at the trackside is increased by typically 0–5 dB. For the lateral vibration of the rail, the effects are much smaller. Once the sound power is known, the sound pressure with the train present can be approximated reasonably well with simple line source directivities.

Numerical models used to predict the sound radiation from railway rails have generally neglected the influence of the ground profile and reflections from the underside of the train body on the sound power and directivity of the rail. These effects are studied in a systematic way including comparisons with measurements.

This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.