John Crank, English mathematician and physicist (d. 2006)

John Crank (6 February 1916 – 3 October 2006) was a distinguished British mathematical physicist whose pioneering contributions significantly advanced the field of numerical analysis, particularly concerning the numerical solution of partial differential equations. His work provided essential tools for tackling complex scientific and engineering problems that are difficult or impossible to solve analytically.

Early Life and Academic Foundations

Born in Hindley, a town in Lancashire, England, John Crank's early life was shaped by the industrial landscape of the region. His father was a carpenter's pattern-maker, a skilled trade that involved creating precise models for castings, perhaps instilling in Crank an early appreciation for precision and structural integrity.

His academic journey began at Manchester University, a renowned institution for scientific research, where he studied from 1934 to 1938. During this period, he distinguished himself by earning both a Bachelor of Science (BSc) and a Master of Science (MSc) degree. He had the unique privilege of studying under two exceptionally influential figures: Sir Lawrence Bragg and Douglas Hartree.

• Sir Lawrence Bragg: A Nobel laureate in Physics (1915, shared with his father, William Henry Bragg, for their work on X-ray diffraction and crystal structure), Bragg's influence likely exposed Crank to the rigorous application of physics to real-world problems.
• Douglas Hartree: A leading figure in numerical analysis and early computing, Hartree was instrumental in the development of computational methods for solving differential equations, laying a crucial groundwork for Crank's future specialisation.

Crank's exceptional academic prowess was further recognised in 1953 when Manchester University awarded him a Doctor of Science (DSc), a higher doctorate typically granted in the UK based on a significant body of original published work that constitutes a substantial contribution to scientific knowledge.

Professional Career and Institutional Leadership

John Crank's professional career spanned significant periods of scientific and industrial change, demonstrating his versatility and leadership capabilities.

During the tumultuous years of the Second World War, Crank applied his mathematical and physical expertise to vital war efforts, working on ballistics. This involved the mathematical modelling of projectile trajectories, a field that heavily relies on the accurate numerical solution of differential equations, thus providing practical experience directly relevant to his later academic research.

Following the war, from 1945 to 1957, he served as a mathematical physicist at the Courtaulds Fundamental Research Laboratory. Courtaulds was a prominent British textile and chemical manufacturer, and its research laboratory was dedicated to advanced scientific inquiry underpinning industrial processes, particularly in materials science and polymer physics. Here, Crank would have encountered diverse problems requiring sophisticated mathematical modelling and computational techniques.

A pivotal moment in his career occurred in 1957 when he was appointed as the inaugural Head of the Department of Mathematics at Brunel College in Acton, London. This marked the beginning of his profound impact on what would later become Brunel University. He played a crucial role in shaping the department and the institution's academic direction. His leadership qualities were further recognised when he served two terms as Vice-Principal of Brunel, contributing significantly to the university's administration and strategic development.

Upon his retirement in 1981, Brunel University bestowed upon him the honorary title of Professor Emeritus, acknowledging his lifelong contributions and continued scholarly association with the institution.

Seminal Contributions to Numerical Analysis: The Crank–Nicolson Method

John Crank's most enduring legacy lies in his profound contributions to the numerical solution of partial differential equations (PDEs), particularly in the context of heat-conduction problems. PDEs are mathematical equations that describe how physical quantities (like temperature, pressure, or fluid velocity) change over time and space, making them fundamental to understanding a vast array of natural phenomena and engineering systems.

While analytical solutions to PDEs are often elusive, especially for complex geometries or boundary conditions, numerical methods provide powerful approximations. Crank focused on developing robust and accurate numerical schemes to solve these challenging equations.

He is pre-eminently known for his collaborative work with Phyllis Nicolson, which led to the development of the revolutionary Crank–Nicolson method. This method, published in 1947, is a finite difference method used for numerically solving the heat equation and similar parabolic partial differential equations. Key features that make it widely adopted include:

• Implicit Scheme: Unlike explicit methods that can suffer from stability issues unless very small time steps are used, the Crank–Nicolson method is an implicit method, meaning it is unconditionally stable for the heat equation, allowing for larger time steps and more efficient computation.
• Second-Order Accuracy: It provides a good balance between accuracy and computational cost, being second-order accurate in both space and time.
• Widespread Application: The Crank–Nicolson method is a cornerstone in computational science and engineering. It is extensively used in fields such as:
  • Heat transfer and thermal engineering (e.g., simulating heat flow in materials, cooling processes).
  • Fluid dynamics (e.g., modelling diffusion processes).
  • Financial mathematics (e.g., pricing options using the Black-Scholes equation).
  • Chemical engineering (e.g., reaction-diffusion systems).

Personal Life and Enduring Legacy

Beyond his formidable academic and scientific pursuits, John Crank was known for his personal interests and commitment to his community. He was an exceptionally keen gardener, demonstrating a meticulousness and appreciation for natural processes that perhaps paralleled his scientific precision. As a lasting retirement gift to Brunel University, he established the John Crank Garden, a tranquil space that stands as a testament to his dedication to the institution and his passion for horticulture.

John Crank was married to his wife, Joan, for 63 years until her passing in 2005. Their long and devoted partnership was a bedrock of his life. They were survived by their two children, carrying forward his family's legacy. John Crank passed away on 3 October 2006, leaving behind a profound impact on numerical analysis and an enduring academic and personal legacy.

Frequently Asked Questions About John Crank

Who was John Crank?

John Crank was a British mathematical physicist (1916–2006) renowned for his significant contributions to the numerical solution of partial differential equations, particularly the development of the Crank–Nicolson method.

What is the Crank–Nicolson method?

The Crank–Nicolson method is a widely used finite difference technique for numerically solving the heat equation and other parabolic partial differential equations. It is valued for its unconditional stability and second-order accuracy, making it efficient for simulating processes like heat conduction and diffusion.

Where did John Crank work and study?

John Crank studied at Manchester University, earning his BSc, MSc, and DSc. Professionally, he worked on ballistics during WWII, as a mathematical physicist at Courtaulds Fundamental Research Laboratory, and most notably, as the first Head of the Department of Mathematics and later Vice-Principal at Brunel College (now Brunel University London).

What is a mathematical physicist?

A mathematical physicist is a scientist who applies rigorous mathematical methods to problems in physics. This field involves developing mathematical frameworks, theories, and computational tools to understand, model, and predict physical phenomena, bridging the gap between theoretical physics and pure mathematics.