Mathematical Physiology II and Mathematical Biology II

I rushed through “Mathematical Physiology II” and have been reading the second volume of “Mathematical Biology II”.

Mathematical Physiology II

This book was beyond my capacity. However, it is well written. The detailed descriptions of the systems covered in this book are excellent, as are the companion diagrams. The circulation, heart, blood, respiratory system, endocrine system, renal system, gastrointestinal system, vision and hearing are covered. The mathematical models and analysis form motivation for imporving my knowledge and understanding. There is (understandable) overlap with the approaches of the Murray (Mathematical Biology). The importance of nondimensionalization, linearization and linear stability analysis are discussed. These approaches are repeatedly used to illustrate features of the models.

Mathematical Biology

I am half way through this book. This is rightly a classic and I am enjoying this second volume more than the first volume. The discussion of spatial patterns in a number of contexts and exploring a number of mechanisms: reaction-diffusion models, mechanical models has been illuminating. The disussion of integumentary patterns: tigers, leopards, fish, snakes (more complex) as well as developmental pattern formation are presented in a consistent manner and the importance of the approaches mentioned above are uniformlu used and the comparison with empirical evidence a common feature.

General Comments

I have frequently posted my commentary about books on “AMazon”. However, the limitations of the (required) ratings are no more evident than when a novice (me) tries to “rate” textbooks. I learned a lot from both these books. They are motivation to improve my education (when time permits)>

Perturbation Methods

This is a concise and precise text. This book amplified my understanding of asymptotics (which is limited) and is an excellent complement to Bender and Orszag.

I found the discussion of the limitation of convergence of series (unless it is extremely rapid), the value of divergent series, the art of the approach by analyzing the behaviour (order) of the functions within sections of the domain helpful conceptually. The more complex middle and end of the book are subjects I hope to return to (this is a personal limitation not a criticism of the book). The first half, however, significantly improved my understanding.

Electromagnetic Vibrations, Waves, and Radiation

This book is some 40 years old. I, however, found it very instructive and enjoyable. It forms part of the Syllabus of the Lewin MIT 8.03 course. I now understand why.  The book is clearly written. The book is filled with worked examples that are interesting and flow from the text. There is consistent explicit use of units and after examples are used they are put in context of the text,

The book covers: oscillations, waves, electromagnetic radiation, transmission of electromagnetic radiation, reflection, refraction, scattering, interaction of electromagnetic fields with matter, diffraction/interference and coherence. This journey is based on classical physics. The authors, however, are quick to point out the limitations of this approach but defend t he practice based on the reasonableness of the approximation for the scale of domain under consideration and the use of expectation values.

The color of the sky, why gold is yellow and silver shiny gray and the frequency dependence of a number of other phenomena as discussed. One example illustrated the tissue penetration of microwave energy into biological tissues. These were all delightful examples.

I am certain that I am completely ignorant of a number of limitations of this book. I also cannot hope to have deep insights into the necessity of quantum mechanics for the nanoscale understanding. However, the clarity and well organized nature of this 40 year old book has certainly diminished my ignorance in a constructive manner.

 

 

Little steps

I have been walking to improve fitness (and perhaps mental health).  An iPhone app Runkeeper allows you to record your GPS position against time and calculates your average speed, pace and “caloric use” (the latter based on a lot of assumptions). The app stores your data and you can review it on web site runkeeper.com.  It allows you to export the data (you go to runkeeper.com/settings  and go to “Export Data” ). A zip file containing the GPS data in GPX format as well as some CSV files containing some of the calculated data.

The web site displays the data in am attractive format. As an exercise in Mathematica I aimed to extract the data from the GPX files and “play” with the data. The graphic that follows is an example.

Not so hidden in plain sight

I have been musing with the Image Processing features of Mathematica. A home maintenance projet provided an opportunity: painting over a repaired wall defect.

I took before and after photographs. The position was not exact and there were some shadowing realted to time of day. However, this still allowed processing. The painting with computer color matched at the hardware store and the whole region was repainted and roughly two layers were applied.

The exercise was to see if the underlying defect could still be detected despite the painting. I used ColorConvert, HistogramTransform (using Manipulate and Slider2D to modify image) and then GradientOrientationFilter.

The results are shown in the graphic below. The top row are the cropped before and after photographs and the corresponding processed images are shown directly below. Note the square defect is easily discernible and the second image of the second row.

Stability, Instability and Chaos

This was a good book. Ir was above my expertise but was instructive nonetheless. It covered the usual value of linearization. It also covered perturbation methods then bifurcation theory (saddlenode, transcritical, pitchfork and Hopf) and then discusses chaos through the horseshoe map concept. I found the discussion of uniomodal maps instructive, particularly unimodal maps without chaos.

I rushed through this book. It was above my head and my rushing reflected my mental state and time commitments. However, despite these caveats with respect to my review, it was a helpful book and motivates me to learn more. The author focuses on concepts and proofs a conceptually constructed. The bibliography is useful.

 

In a Spin

I have been contemplating the Coriolis effect. In the above diagram the blue axes are an inertial reference frame with the blue arrows representing the unit vectors. The red arrows show an instant from a rotating reference frame.

The following shows the derivation of the Coriolis and centrifugal “fictitious” forces terms. Considere.g. ( )