The books once interested me

coolboy

In the previous post (#112), I listed two books:

van de Hulst, H. C., 1980: Multiple Light Scattering: Tables Formulas and Applications, Volumes I and II. Academic Press, New York, 739 pp.
Chandrasekhar, S., 1950: Radiative Transfer. Oxford Univ. Press, 393 pp. (Reprinted by Dover.)

The follow-up discussion had been along the line of S. Chandrasekhar. I now return to van de Hulst. I believe the most interesting and important contribution van de Hulst made to the field of radiative transfer was the development of adding/doubling method. The radiative transfer equation including scattering processes is an integro-differential equation. The usual approach of solving this type of equations is to discretize the integral part (by finite difference or spectral expansion) and convert the integro-differential equation into a set of differential equations. van de Hulst (1963) proposed a new method of solving the radiative transfer equation called adding/doubling method that was completely different from the traditional thinking of solving an equation:

van de Hulst, H. C., 1963: A New Look at Multiple Scattering. Sci. Rep., 81 pp. NASA, Goddard Inst. Space Studies, New York

This was only an internal report that was not available to public. It appears that the first formal publication of the adding/doubling method appeared in the following book:

Brandt, J. C., and M. B. McElroy (eds), 1968: The Atmospheres of Venus and Mars. Gordon and Breach, New York, 288 pp.

The above book summarized the scientific knowledge of the atmospheres of Venus and Mars at the dawn of the planetary exploration age. However, many people including myself were interested in the book only because of van de Hulst’s paper in the book that introduced the adding/doubling method:

van de Hulst, H. C., and K. Grossman, 1968: Multiple light scattering in planetary atmospheres, in The Atmospheres of Venus and Mars, edited by J. C. Brandt and M. B. McElroy, p. 35-55, Gordon and Breach, New York.

coolboy

The scientific results of several spacecraft missions to Venus were summarized in the following book on my bookshelves:

Bougher, S. W., D. H. Huntern, and R. J. Phillips (Eds.), 1997: Venus II. Geology, Geophysics, Atmosphere, and Solar Wind Environment. The Univ. of Arizona Press, Tucson, 1362 pp.

coolboy

I once said that there were many more similarities between Earth and Mars than between Earth and Venus. The following monograph attempts to predict Martian climate based on our understanding to the Earth’s climate:

Read, P. L., and S. R. Lewis, 2004: The Martian Climate Revisited. Atmosphere and Environment of a Desert Planet. Springer, New York, 326 pp.

coolboy

The Earth’s atmosphere is one of the planetary atmospheres in the solar system. Comparing to all the other planetary atmospheres, the investigation of Earth’s atmosphere has a very long history and the field has been investigated extensively. As a result, people usually do not categorize the investigation of Earth’s atmosphere into the field of planetary atmospheres. However, the following book was generally also considered to be a textbook for planetary atmospheres though it only discussed the evolution of the Earth’s atmosphere:

Walker, J., 1975: Evolution of the Atmosphere.  Macmillan Publishing Co., Inc., New York, 318 pp.

coolboy

Mercury, Venus, Earth and Mars are called terrestrial planets in the solar system whereas Jupiter, Saturn, Uranus and Neptune are called giant planets. A good introductory book on the giant planets on my bookshelves is:

Irwin, P. G. J., 2003: Giant Planets of Our Solar System: Atmospheres, Composition and Structure. Springer-Verlag, New York, 361 pp.

周华

coolboy 发表于 2018-3-14 04:16
Mercury, Venus, Earth and Mars are called terrestrial planets in the solar system whereas Jupiter, S ...

这本书里的图片是黑白的，要是彩色的就漂亮多了。

coolboy

周华 发表于 2018-3-14 08:40
这本书里的图片是黑白的，要是彩色的就漂亮多了。

The fact that there are no color plots in the book is an indication of a high-level professional monograph though it still belonged to an introductory book to the field. On the other hand, many textbooks for undergraduate students usually contain many color plots in order to attract attention from young students. For example, the following (most) popular textbook for undergraduate students to the field of planetary science contains many color plots:

Kelly Beatty, J. and A. Chaikin (editors), 1990: The New Solar System. Third Edition (Introduction by Carl Sagan). Cambridge Univ. Press, 326 pp.

coolboy

Add two monographs on the topic of laser ablation that I have been reading recently:

Bauerle, D., 2011: Laser Processing and Chemistry. Fourth Edition. Springer-Verlag, New York, 851 pp.
Grigoropoulos, C. P., 2009: Transport in Laser Microfabrication: Fundamentals and Applications. Cambridge Univ. Press, Cambridge, 400 pp.

coolboy

I just completed a research paper in which I believe the following cited books have not been listed previously:

Abramowitz, M. J. and I. A. Stegun, 1965: Handbook of Mathematical Functions. Dover, New York, 1046 pp.
Anisimov, S. I., and V. A. Khokhlov, 1995: Instabilities in Laser-Matter Interaction. CRC Press, London, 147 pp.
Zel’dovich, Ya. B., and Yu. B. Raizer, 1966: Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. New York, Academic Press, 916 pp.

coolboy

Recently, I have been refreshing my memory or reviewing my knowledge on the conformal mapping of complex variables. The textbooks on the subject on my bookshelves are:

Conway, J. B., 1978: Functions of One Complex Variable. Second Edition. Springer-Verlag, New York, 317 pp.
Churchill, R. V. and J. W. Brown, 1990: Complex Variables and Applications. Fifth Edition. McGraw-Hill Book Company, New York, 361 pp.

The first book by Conway was highly mathematical and was clearly for students majoring in mathematics. It only contains a few page describing conformal mapping. The second book was a good textbook for students majoring science and engineering. It has about 100 pages containing detailed explanatory descriptions and many worked out examples of the conformal mapping. It was interesting to find that the first book contained two relatively long sections on “The gamma function” and “The Riemann zeta function”. Thus, the knowledge of “Special functions” in mathematical physics is supposed to be taught in the course of complex variables. Obviously, “The Riemann Hypothesis” was also markedly introduced. The important relation between the Riemann hypothesis and prime numbers is the Euler’s Theorem.

The motivation of reviewing conformal mapping was related to a project I involved recently that contains the boundary fitted coordinate transformation in a CFD model. One reference book on this subject is:

Thompson, J. F., Z. U. A. Warsi, C. W. Mastin, 1985: Numerical Grid Generation: Foundations and Applications. Elsevier Science Publishing Co., Inc., 327 pp.

coolboy

The field of “solitons” or “solitary waves” was developed originally in fluid mechanics and, actually, my first science paper was about solitary waves in the Earth’s atmosphere. The field was getting very hot in 1960s-1980s after people discovered that a large class of nonlinear partial differential equations associated with “solitons” can be solved by the so-called inverse scattering method. At the time, almost all the historical reviews on “solitons” would mention one famous example of the accidental discovery of “solitons” in numerical solution of KdV equation for the “Fermi-Pasta-Ulam” model developed in the field of solid mechanics (e.g., Drazin and Johnson 1989). Recently, I read a book by Nesterenko (2001) on solid mechanics. I finally understood what the “Fermi-Pasta-Ulam” model was about and how the KdV equation in an anharmonic lattice was derived. Apparently, V. F. Nesterenko was famous in the field of “solitons” in solid mechanics because he systematically developed and explored many equations having solitons as their solutions for the “granular materials” in solid mechanics. However, he seemed weak in applied mathematics so all his theoretical investigations on solitons were only for special solutions of “traveling waves”, which was only the first-step or preliminary study to solitons. He named those traveling wave solutions to be “stationary solutions”, which I think is inappropriate. The partial differential equations describing solitons in solid mechanics were derived from sets of ordinary differential equations. In other words, the generic equations describing the solitons in solid mechanics were actually ordinary differential equations. Since it is much easier and more accurate to numerically solve ordinary differential equations than partial differential equations, various behaviors of solitons including interaction among different solitons can be more efficiently simulated numerically in solid mechanics.

Drazin, P. G., and R. S. Johnson, 1989: Soliton: an Introduction. Cambridge Univ. Press, 226 pp.
Nesterenko, V. F., 2001: Dynamics of Heterogeneous Materials. Springer-Verlag, New York, 510 pp.

coolboy

The so-called “inverse scattering method” to solve a large class of partial differential equations associated with “solitons” is to convert the nonlinear differential equation into a second order linear equation related to the scattering problem. That famous transformation (Backlund transformation) was similar to or basically the same as the one to solve the nonlinear Riccati equation I described previously (post: 100#). The same kind of transformation can also be used to solve the famous Burgers equation that contains both the nonlinear advection and linear diffusion terms. In this case, the Backlund transformation converts the nonlinear Burgers equation into a linear heat conduction equation, which can be solved exactly. The Burgers equation also contains the “solitary waves” as its solutions. However, the shape of those solitary waves shows an asymmetric feature so the solutions are usually not called “solitons” but called “humps”. The degree of the asymmetry depends on the magnitude of the Reynolds number of the fluid. A larger Reynolds number leads to a stronger asymmetry of the “hump”. The following book gives a comprehensive overview on the Burgers equation and its generalization:

Sachdev, P. L., 1987: Nonlinear Diffusive Waves. Cambridge Univ. Press, Cambridge, 246 pp.

coolboy

I also have the following three books on solitary waves on my book shelves:

[1] Lamb, G. L., Jr., 1980: Elements of Soliton Theory. John Wiley & Sons, New York, 289 pp.
[2] 谷内俊弥，西原功修（徐福元等译），1981：非线性波动。原子能出版社。（1.15元）
[3] 郭柏灵编著，1995：非线性演化方程。上海科技教育出版社。（18.70元）

In principle, many nonlinear evolution equations have been solved once they are transformed into linear equations describing the scattering processes. In practice, there still exist many technical details on how to solve those linear equations by the “inverse scattering method”. The first book [1] by Lamb provided a detailed description on how to solve the scattering and inverse scattering problems. Book [2] was a textbook on nonlinear waves for graduate students in physics major. Book [3] is highly mathematical and focused on the qualitative and asymptotic properties of the nonlinear evolution equations.

coolboy

I mentioned scattering and inverse scattering method while talking about solving the nonlinear evolution equations above. I listed two books before (posts: 112#, 120#) that described the light scattering by small particles:

van de Hulst, H. C., 1957: Light Scattering by Small Particles. John Wiley & Sons, Inc., New York, 470 pp, (Reprinted by Dover).
Bohren, C. F. and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. John Wiley & Sons, Inc., 530 pp.

In this treatment, the light was described by electromag_n_e_t_i_c waves and the scatter processes are described by classic electromag_n_e_t_i_c wave theory. On the other hand, the scattering and inverse scattering associated with solitons refer to the quantum treatment of the dispersal of a beam of particles by an object. It generally belongs to an intermediate or advanced level of quantum mechanics courses. The following two books provide systematic descriptions on scattering and inverse scattering techniques:

Landau, R., 1996: Quantum Mechanics II. A Second Course in Quantum Theorey. Second Edition. John Wiley & Sons, New York, 496 pp.
Chadan, K., and P. C. Sabatier, 1977: Inverse Problems in Quantum Scattering Theory. Springer-Verlag, New York, 344 pp.

coolboy

A few popular books on inversion or retrieval theories and applications in geophysics or atmospheric science:

Hanel, R. A., b. J. Conrath, D. E. Jennings, and R. E. Samuelson, 1992: Exploration of the Solar System by Infrared Remote Sensing. Cambridge Univ. Press, Cambridge, 458 pp.
Houghton, J. T., F. W. Taylor and C. D. Rodgers, 1984: Remote Sounding of Atmospheres. Cambridge Univ. Press, 343 pp.
Menke, W., 1989: Geophysical Data Analysis: Discrete Inverse Theory. Revised Edition. Academic Press, Inc., 289 pp.
Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding, Theory and Practice. World Scientific, London, 238 pp.
Twomey, S., 1970: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurement. Elsevier, Amsterdam, 243 pp.


In general, given known parameters such as the properties of materials or localized relationships among different parameters, a forward problem describes a spatial relationship and its temporal evolution of the physical state. On the other hand, an inverse or a retrieval problem is to find the values of those parameters or the localized relationship among different parameters built into those equations describing the forward problems.

For example, in the field of fluid mechanics or gasdynamics, the so-called Rankine-Hugoniot relations describe the mass, momentum and energy conservation laws across a shock. Given the values of gas constants and the localized equation of state (p=rho*R*T or p=(gamma-1)*rho*E for ideal gas) Rankine-Hugoniot relations can be used to solve many forward problems such as design good numerical schemes to solve the Euler equations. In the field of solid mechanics, on the other hand, Rankine-Hugoniot relations are often or also used to derive the localized equation of state, i.e., to find the parametric relationship between pressure and density for different materials. This is clearly an inverse problem. Here is a book that contains an overview on this subject:

Asay, J. R., and M. Shahinpoor (editors), 1993: High-Pressure Shock Compression of Solids. Springer Science+Business Media, LLC, 393 pp.