astronomy

I – Shih Liu

I – Shih Liu is a astronomy 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 I – Shih Liu rather than just read about it. In short: I – Shih Liu (1943) is a Taiwanese civil engineer. He teaches at the Institute of Mathematics of Federal University of Rio de Janeiro.

Key takeaways

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

Reference excerpt

I – Shih Liu (1943) is a Taiwanese civil engineer. He teaches at the Institute of Mathematics of Federal University of Rio de Janeiro.

Education I – Shih Liu studied at the National Taiwan University and graduated with a diploma in 1972. He continued his studies at the Johns Hopkins University (JHU) where he received his doctorate in applied mechanics in 1972 under the supervision of Ingo Müller.

Academic life He became assistant professor at the National Taiwan University in 1965, teaching and research assistant at the Johns Hopkins University in 1967, post-doctoral fellow in 1972 and professor at Federal University of Rio de Janeiro (UFRJ) in 1972. He became visiting professor at Carnegie Mellon University in 1976–1977, at University of Bologna in 1982, 1986, at University of Berlin in 1990-1991 and Nagoya Institute of Technology in 2004. He also became visiting professor at Texas A&M University in 2006–2007, at College of Earth Sciences National Central University in 2012 and director pro-tempore at UFRJ in 2000–2002. Since 1972, he has more than 50 mathematical research articles published in peer-reviewed international journals. He is married with one son.

Research areas His work deals with continuum mechanics, thermodynamics, relativistic mechanics, rigid body mechanics, elastodynamics, mechanics of deformable bodies, constitutive theories, entropy principle, Lagrange multipliers.

Writings Introduction to Continuum Mechanics, Springer-Verlag, 2002 with Jose Merodio e Giuseppe Saccomandi: Constitutive Theories: Basic Principles Chapter 6 in Continuum Mechanics, in Encyclopedia of Life Support Systems (EOLSS) Developed under the auspices of the UNESCO Publications, 2009 A Continuum Mechanics Primer Lecture Note - On Constitutive Theories of Materials, 2010 Archived 5 July 2022 at the Wayback Machine Introduction to Continuum Mechanics Lecture Note, 2018 Elementary Tensor Analysis Lecture Note, 2018

Selected publications Liu, I.-S. (1972): Method of Lagrange Multipliers for Exploitation of the Entropy Principle | Arch. Rat. Mech. Anal. (ARMA); vol. 46, no. 2, pp. 131–148. Doi:10.1007/BF00250688 Liu, I.-S. (1973): (a) A Non-Simple Heat-Conducting Fluid | Arch. Rat. Mech. Anal. (ARMA); vol. 50, no. 1, pp. 26–33. Doi:10.1007/BF00251292 Liu, I.-S. (1973): (b) On the Entropy Supply in a Classical and a Relativistic Fluid | Arch. Rat. Mech. Anal. (ARMA); vol. 50, no. 2, pp. 111–117. Doi:10.1007/BF00249878 Liu, I.-S. (1982): On Representations of Anisotropic Invariants | Int. J. Eng. Sci. (IJES); vol. 20, no. 10, pp. 1099–1109. Doi:10.1016/0020-7225(82)90092-1 Liu, I.-S. (1996): On Entropy Flux-Heat Flux Relation in Thermodynamics with Lagrange Multipliers | Cont. Mech. Thermodyn. (CMT); vol. 8, pp. 247–256. Doi:10.1007/s001610050042 Liu, I.-S. (2001): Constitutive Equations of Extended Thermodynamics from a Hybrid Pair of Generator Functions | Cont. Mech. Thermodyn. (CMT); vol. 13, no. 1, pp. 25–39. Doi:10.1007/s001610100040 Liu, I.-S. (2003): On the Transformation Property of the Deformation Gradient under a Change of Frame | J. Elast. (JELAS); vol. 71, no. 1, pp. 73–80. Doi:10.1023/B:ELAS.0000005548.36767.e7 Liu, I.-S. (2005): Further Remarks on Euclidean Objectivity and the Principle of Material Frame-Indifference | Cont. Mech. Thermodyn. (CMT); vol. 17, no. 2, pp. 125–133. Doi:10.1007/s00161-004-0191-3 Liu, I.-S. (2008): Entropy Flux Relation for Viscoelastic Bodies | J. Elast. (JELAS); vol. 90, no. 3, pp. 259–270. doi:10.1007/s10659-007-9142-0 Liu, I.-S. (2009): (a) Constitutive Theory of Anisotropic Rigid Heat Conductors | J. Math. Phys. (JMP); vol. 50, no. 8, pp. 083506. Doi:10.1063/1.3190487 Liu, I.-S. (2009): (b) On Entropy Flux of Transversely-Isotropic Elastic Bodies | J. Elast. (JELAS); vol. 96, no. 2, pp. 97–104. Doi:10.1007/s10659-009-9200-x Liu, I.-S. (2011): Successive Linear Approximation for Boundary Value Problems of Nonlinear Elasticity in Relative-Descriptional Formulation | Int. J. Eng. Sci. (IJES); vol. 49, no. 7, pp. 635–645. Doi:10.1016/j.ijengsci.2011.02.006 Liu, I.-S. (2012): A Note on the Mooney–Rivlin Material Model | Continuum Mech. Thermodyn.; vol. 24, no. 4, pp. 583–590. Doi:10.1007/s00161-011-0197-6 Liu, I.-S. (2014): A Solid-Fluid Mixture Theory of Porous Media | Int. J. Eng. Sci. (IJES); vol. 84, pp. 133–146.Doi:10.1016/j.ijengsci.2014.07.002

External links Home page Archived 21 May 2023 at the Wayback Machine at DMM

References

Worked examples

Example 1 — a first encounter with I – Shih Liu

Start with the simplest possible case. Write down what I – Shih Liu claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 I – Shih Liu 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 I – Shih Liu 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 I – Shih Liu

In research: I – Shih Liu appears in astronomy 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 I – Shih Liu 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: I – Shih Liu is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1943 births, Academic staff of the Federal University of Rio de Janeiro, Johns Hopkins University alumni, so understanding it makes those chapters shorter.
In everyday life: Look for I – Shih Liu 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 I – Shih Liu in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what I – Shih Liu 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.
Explain I – Shih Liu out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is I – Shih Liu in simple terms?

I – Shih Liu (1943) is a Taiwanese civil engineer. He teaches at the Institute of Mathematics of Federal University of Rio de Janeiro.

Why does I – Shih Liu matter?

Because it connects several astronomy 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 I – Shih Liu?

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 I – Shih Liu.