Propagation of radio frequency (RF) electromagnetic waves becomes infeasible in certain situations, thus resulting in "RF-denied" environments. Examples include underground and deep-water facilities (mines, shelters, storage areas, tunnels, submarines, undersea cables, etc.). Recent events have highlighted the importance of wireless communications with such environments. A prominent example is the July 2018 rescue of a soccer team from the Tham Luang Nang Non cave in Thailand after they had been trapped underground for over two weeks. Such RF-denied environments are fundamentally produced by the short "skin depth" of electromagnetic waves within conductive media such as earth or seawater, which results in high attenuation. Fortunately, the skin depth increases as the frequency decreases, so extremely low frequency (ELF) radio waves in the kHz range can penetrate long distances in nominally RF-denied environments. For example, the skin depth in sea water is 7.1 m at 1 kHz, which would allow undersea communications to depths of about 30 m with reasonable transmit power levels if one could effectively couple ELF radio waves into the medium. However, conventional antennas are extremely large and impossible to deploy in this frequency range, while electrically-short antennas have very poor power efficiency. This project seeks to solve this fundamental problem by adopting a radically new approach to ELF antennas that is based on the mechanical motion of permanent magnets. The proposed research will have a broad impact on the availability of bidirectional wireless communications in RF-denied environments. Specifically, it will enable low-data-rate wireless links to be established using portable, robust, low-power, and low-cost devices. Such links are expected to have a multitude of applications in fields such as sensing and networking in underwater or underground environments, near-surface geophysics, atmospheric science, search and rescue operations, mining, and oil and gas exploration.The availability of portable low-power ELF transceivers would immediately enable communications within RF-denied environments by enabling bidirectional low-data-rate wireless links with the surface. While miniaturized and highly-sensitive ELF receivers are available, ELF transmitters (typically dipole or loop antennas) are the key obstacles for realizing such links since they are physically large and power-hungry. Thus, this project focuses on miniaturized and power-efficient ELF transmitters that enable bidirectional communications over short- and medium-range (up to about 1 km) wireless links in conductive media. In particular, the proposed research will explore a fundamentally new all-mechanical approach to ELF transmitter design that has the potential to enable efficient use of this region of the EM spectrum. The major intellectual contributions of this project focus on different aspects of this overall approach. They include: i) Proposing the concept of distributed all-mechanical transmitters based on synchronization over either wired or wireless networks and showing how it overcomes the key limitations of existing ELF transmitter architectures; ii) Creating a theoretical basis for the design of power-efficient wireless communications using systems that have significant mechanical inertia, thus linking the mathematics of information transfer over fading channels to the physics of the mechanical devices; and iii) Laying the first theoretical groundwork for the precise control of networked high-speed machines, which has the potential to dramatically advance the current state of the art by seamlessly modeling complex 3-D (dimensional) machine parameter variations and their tight coupling with high-speed machine vibrations and energy/power fluctuations within the transmitter network.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.