Students studying electromagnetism, signal processing, or numerical simulation
Engineers exploring signal transmission in conductive media
Data scientists working with physics-generated structured data
Researchers interested in executable reconstructions of historical experiments
Educators integrating computational laboratories into coursework

It provides a reproducible computational environment for studying signal transmission through conductive media, bridging physical modeling, circuit abstraction, and time-domain system behavior.

Abstract

This dataset provides a computational reconstruction of S. J. M. Bear's 1884 experiment "Telegraphing Without Wires," originally presented before the American Institute of Electrical Engineers. The project transforms a pre-digital manuscript — written decades before computers and numerical modeling — into a fully reproducible finite-difference simulation framework. By solving the variable-conductivity Laplace equation, it enables quantitative analysis of electric potential fields, current density distributions, and receiver behavior in conductive media.

The dataset includes multi-scenario simulations with spatially varying conductivity (uniform media, freshwater–brine interfaces, insulating obstacles, conductive paths, and localized plumes). Receiver behavior is modeled using a Thevenin-equivalent formulation with relay resistance and threshold dynamics. Time-domain simulations capture keying signals, electrode polarization effects, and relay actuation.

Beyond historical reconstruction, this resource serves as an educational and research platform:

For students: a hands-on bridge between electromagnetic theory, partial differential equations, numerical methods, and signal processing.
For engineers: a sandbox for studying signal transmission in conductive environments (e.g., underwater communication, geophysical sensing, bioelectric systems).
For data scientists: structured, multi-modal datasets suitable for statistical modeling, inverse problems, parameter estimation, surrogate modeling, and machine learning experiments on physics-generated data.

All outputs are provided in CSV, JSON, and compressed NumPy formats to support reproducibility and downstream analysis. The included Python source code regenerates all scenarios.

Dataset Structure

Each experiment generates:

File	Description
`*_fields.npz`	Spatial field arrays (potential, electric field, current density)
`*_timeseries.csv`	Time-domain signal and relay behavior
`*_summary.json`	Per-experiment scalar results and circuit parameters
`figs/`	Figures directory

Global outputs:

File	Description
`experiment_summary_v1p1.csv`	Aggregated scalar results across all experiments
`experiment_summary_v1p1.json`	JSON equivalent of the above
`sweep_sigma_v1p1.csv`	Conductivity sweep results
`sweep_sigma_v1p1.json`	JSON equivalent of the sweep
`manifest_v1p1.json`	File inventory and checksums
`run_meta_v1p1.json`	Run metadata (version, timestamp, grid parameters)

NPZ File Specification (`*_fields.npz`)

Material Map

Array	Type	Description
`sigma`	2D float	Spatial conductivity map of the tub. Higher values indicate more conductive regions; lower values indicate less conductive or insulating regions.

Base 1-Volt Sending Condition

Array	Type	Description
`V_tub_1V`	2D float	Potential distribution when 1 volt is applied across the sending electrodes.
`Ex_1V`	2D float	Horizontal component of the electric field under the 1-volt sending condition.
`Ey_1V`	2D float	Vertical component of the electric field under the 1-volt sending condition.
`Emag_1V`	2D float	Magnitude of the electric field at each spatial location.
`Jx_1V`	2D float	Horizontal component of current density.
`Jy_1V`	2D float	Vertical component of current density.
`Jmag_1V`	2D float	Magnitude of current density.

Delivered Voltage Fields

Array	Type	Description
`V_delivered_no_pol`	2D float	Potential distribution accounting for battery internal resistance and contact resistance, without polarization.
`V_delivered_pol`	2D float	Potential distribution including steady-state electrode polarization effects.

Receiver-Port Solution

Array	Type	Description
`V_port_1V`	2D float	Potential distribution when 1 volt is applied directly across the receiver electrodes. Used to estimate the receiver's effective resistance.

Electrode Masks

Binary arrays (0 or 1):

Array	Description
`tx_plus`	Positive sending electrode region
`tx_minus`	Negative sending electrode region
`rx1`	First receiver electrode
`rx2`	Second receiver electrode

Time-Series CSV Specification (`*_timeseries.csv`)

Column	Description
`t`	Simulation time in seconds
`key`	Telegraph key state (1 = pressed, 0 = released)
`Vpol`	Electrode polarization voltage
`Vtub`	Voltage delivered across the tub
`Isource`	Current supplied by the battery
`Vth`	Effective voltage at the receiver
`Irelay`	Current flowing through the relay
`relay_state`	Relay state (1 = closed, 0 = open)

Per-Experiment Summary JSON Fields (`*_summary.json`)

Field	Description
`name`	Experiment identifier
`sigma_map_name`	Conductivity scenario used
`battery_voltage`	Battery voltage
`battery_internal_resistance_ohm`	Internal battery resistance
`electrode_contact_resistance_ohm`	Electrode contact resistance
`relay_resistance_ohm`	Relay resistance
`relay_pull_in_current`	Current required to activate relay
`relay_release_current`	Current below which relay releases
`Vth_per_1V`	Receiver voltage scaling factor
`Rth_ohm_like`	Effective resistance at receiver port
`delivered_tub_voltage_no_pol`	Tub voltage without polarization
`delivered_tub_voltage_with_pol`	Tub voltage with polarization
`Irelay_no_pol`	Relay current without polarization
`Irelay_with_pol`	Relay current with polarization
`relay_click_no_pol`	Relay activation without polarization (bool)
`relay_click_with_pol`	Relay activation with polarization (bool)
`tub_resistance_ohm_like`	Effective tub resistance
`source_current_no_pol`	Battery current without polarization
`source_current_with_pol`	Battery current with polarization

Conductivity Sweep Dataset (`sweep_sigma_v1p1.csv`)

Column	Description
`sigma`	Uniform conductivity value
`R_tub`	Effective tub resistance
`Vth_per_1V`	Receiver scaling factor
`Rth`	Effective receiver resistance
`Vtub_no_pol`	Delivered voltage without polarization
`Irelay_no_pol`	Relay current without polarization
`click_no_pol`	Relay activation without polarization (0/1)
`Vtub_pol`	Delivered voltage with polarization
`Irelay_pol`	Relay current with polarization
`click_pol`	Relay activation with polarization (0/1)

Reproducibility

Run:

python Bear-1884-Code-v1.1.py

Outputs are generated under:

output/
output/figs/

Dependencies:

numpy
scipy
matplotlib

Contribution

Developed by DBbun LLC, this project demonstrates how a historical scientific experiment can be transformed into a structured, reproducible computational laboratory suitable for education, engineering analysis, and data-driven research.

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Telegraphing Without Wires (1884) — Finite-Difference Simulator and Synthetic Dataset Reconstruction

Who Should Use This Dataset