mathematics

Michael Cates

Michael Cates is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Michael Cates rather than just read about it. In short: Michael Elmhirst Cates (born 5 May 1961) is a British physicist. He is the 19th Lucasian Professor of Mathematics at the University of Cambridge and has held this position since 1 July 2015.

Key takeaways

Michael Cates belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Michael Cates to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Michael Cates from memory before moving on to harder problems.

Reference excerpt

Michael Elmhirst Cates (born 5 May 1961) is a British physicist. He is the 19th Lucasian Professor of Mathematics at the University of Cambridge and has held this position since 1 July 2015. He was previously professor of natural philosophy at the University of Edinburgh, and held a Royal Society Research Professorship from 2007 to 2022. His work focuses on the theory of soft matter, such as polymers, colloids, gels, liquid crystals, and granular material. A recurring goal of his research is to create a mathematical model that predicts the stress in a flowing material as a functional of the flow history of that material. Such a mathematical model is called a constitutive equation. He has worked on theories of active matter, particularly dense suspensions of self-propelled particles which can include motile bacteria. His interests also include fundamental field theories of active systems in which time-reversal symmetry (T-symmetry, and more generally, CPT symmetry) is absent. Such theories are characterised by non-zero steady-state entropy production. His recent work has focussed on phase separation in active systems, including phenomena such as nucleation, interfacial fluctuations, and wetting. At Edinburgh, Cates was the principal investigator of an EPSRC Programme Grant, awarded in 2011, entitled Design Principles for New Soft Materials. On his departure for Cambridge, Cait MacPhee took over as principal investigator until conclusion of the grant in 2017. Cates remains an honorary professor at Edinburgh, where he serves on the advisory board of the Higgs Centre for Theoretical Physics.

Early life Cates was born on 5 May 1961. He read Natural Sciences and earned a PhD at Trinity College, Cambridge, in 1985, where he studied with Sam Edwards.

Academic career Cates was a research fellow and lecturer at the Cavendish Laboratory, University of Cambridge before moving to Edinburgh in 1995.

Honours Cates won the Bingham Medal of the US Society of Rheology in 2016. He had previously won the 2013 Weissenberg Award of the European Society of Rheology and the 2009 Gold Medal of the British Society of Rheology. He was awarded the 2009 Dirac Prize by the Institute of Physics. He won the 1991 Maxwell Medal and Prize. He has served as an elected member of the Council of the Royal Society; as chair of the International Scientific Committee of ESPCI ParisTech, and as a Trustee of The Cyprus Institute. He was an honorary fellow of Trinity College, Cambridge from 2013 until 2016, when he became instead a senior research fellow. Cates was elected a member of the National Academy of Engineering in 2019 for research on the rheology, dynamics, and thermodynamics of complex fluids, and for scientific leadership in the European Community. In 2021 he was elected an International Member of the US National Academy of Sciences.

Works Michael Cates has over 400 refereed scientific publications, with over 50,000 citations. His h-index is 118. Publications include:

Milner, S. T.; Witten, T. A.; Cates, M. E. (1988). "Theory of the grafted polymer brush". Macromolecules. 21 (8). American Chemical Society (ACS): 2610–2619. Bibcode:1988MaMol..21.2610M. doi:10.1021/ma00186a051. ISSN 0024-9297. Cates, M E; Candau, S J (20 August 1990). "Statics and dynamics of worm-like surfactant micelles". Journal of Physics: Condensed Matter. 2 (33). IOP Publishing: 6869–6892. doi:10.1088/0953-8984/2/33/001. ISSN 0953-8984. S2CID 250743546. Cates, M. E. (1987). "Reptation of living polymers: dynamics of entangled polymers in the presence of reversible chain-scission reactions". Macromolecules. 20 (9). American Chemical Society (ACS): 2289–2296. Bibcode:1987MaMol..20.2289C. doi:10.1021/ma00175a038. ISSN 0024-9297. Sollich, Peter; Lequeux, François; Hébraud, Pascal; Cates, Michael E. (10 March 1997). "Rheology of Soft Glassy Materials". Physical Review Letters. 78 (10). American Physical Society (APS): 2020–2023. arXiv:cond-mat/9611228. Bibcode:1997PhRvL..78.2020S. doi:10.1103/physrevlett.78.2020. ISSN 0031-9007. S2CID 14392727. Cates, M. E.; Wittmer, J. P.; Bouchaud, J.-P.; Claudin, P. (31 August 1998). "Jamming, Force Chains, and Fragile Matter". Physical Review Letters. 81 (9). American Physical Society (APS): 1841–1844. arXiv:cond-mat/9803197. Bibcode:1998PhRvL..81.1841C. doi:10.1103/physrevlett.81.1841. ISSN 0031-9007. S2CID 119378758. Pham, K. N. (5 April 2002). "Multiple Glassy States in a Simple Model System". Science. 296 (5565). American Association for the Advancement of Science (AAAS): 104–106. Bibcode:2002Sci...296..104P. doi:10.1126/science.1068238. ISSN 0036-8075. PMID 11935020. S2CID 34313265. Stratford, K. (30 September 2005). "Colloidal Jamming at Interfaces: A Route to Fluid-Bicontinuous Gels". Science. 309 (5744). American Association for the Advancement of Science (AAAS): 2198–2201. arXiv:cond-mat/0510040. Bibcode:2005Sci...309.2198S. doi:10.1126/science.1116589. ISSN 0036-8075. PMID 16195456. S2CID 14719880. Tailleur, J.; Cates, M. E. (29 May 2008). "Statistical Mechanics of Interacting Run-and-Tumble Bacteria". Physical Review Letters. 100 (21) 218103. arXiv:0803.1069. Bibcode:2008PhRvL.100u8103T. doi:10.1103/physrevlett.100.218103. ISSN 0031-9007. PMID 18518641. S2CID 9651052. Wyart, M.; Cates, M. E. (6 March 2014). "Discontinuous shear thickening without inertia in dense non-Brownian suspensions". Physical Review Letters. 112 098302. arXiv:1311.4099. doi:10.1103/PhysRevLett.112.098302. Fodor, E.; Nardini, C.; Cates, M. E.; Tailleur, J.; Visco., P.; van Wijland, F. (13 July 2016). "How far from equilibrium is active matter?". Physical Review Letters. 117 038103. arXiv:1604.00953. doi:10.1103/PhysRevLett.117.038103. Tjhung, E.; Nardini, C.; Cates, M. E. (24 September 2018). "Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process". Physical Review X. 112 031080. arXiv:1801.07687. doi:10.1103/PhysRevX.8.031080.

References

External links Media related to Michael Cates at Wikimedia Commons

Illustrations

Worked examples

Example 1 — a first encounter with Michael Cates

Start with the simplest possible case. Write down what Michael Cates claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Michael Cates before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Michael Cates ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Michael Cates

In research: Michael Cates appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Michael Cates in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Michael Cates is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, Academics of the University of Edinburgh, Alumni of Trinity College, Cambridge, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Cates outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Michael Cates in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Michael Cates means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
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Frequently asked questions

What is Michael Cates in simple terms?

Michael Elmhirst Cates (born 5 May 1961) is a British physicist. He is the 19th Lucasian Professor of Mathematics at the University of Cambridge and has held this position since 1 July 2015.

Why does Michael Cates matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Michael Cates?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Michael Cates.