# Plant Physics

From Galileo, who used the hollow stalks of grass to demonstrate the idea that peripherally located construction materials provide most of the resistance to bending forces, to Leonardo da Vinci, whose illustrations of the parachute are alleged to be based on his study of the dandelion’s pappus and the maple tree’s samara, many of our greatest physicists, mathematicians, and engineers have learned much from studying plants.

*Plant Physics*. The result of a long-term collaboration between plant evolutionary biologist Karl J. Niklas and physicist Hanns-Christof Spatz,

*Plant Physics*presents a detailed account of the principles of classical physics, evolutionary theory, and plant biology in order to explain the complex interrelationships among plant form, function, environment, and evolutionary history. Covering a wide range of topics—from the development and evolution of the basic plant body and the ecology of aquatic unicellular plants to mathematical treatments of light attenuation through tree canopies and the movement of water through plants’ roots, stems, and leaves—

*Plant Physics*is destined to inspire students and professionals alike to traverse disciplinary membranes.

**J. Z. Kiss, Miami University | Choice**

**Maciej Zwieniecki, Harvard University | Quarterly Review of Biology**

**Plant Science Bulletin**

**R. S. Shorter, Winchester College | Contemporary Physics**

*Plant Physics*] will inspire and interest as well as provide a rock solid foundation for further study.”

**Steven Vogel, Duke University**

**Lorna Gibson, Massachusetts Institute of Technology**

1.1 What is plant physics?

1.2 The importance of plants

BOX 1.1 The amount of organic carbon produced annually

1.3 A brief history of plant life

1.4 A brief review of vascular plant ontogeny

1.5 Plant reproduction

1.6 Compromise and adaptive evolution

BOX 1.2 Photosynthetic efficiency versus mechanical stability

1.7 Elucidating function from form

1.8 The basic plant body plans

1.9 The importance of multicellularity

CHAPTER 2. Environmental Biophysics

2.1 Three transport laws

2.2 Boundary layers

2.3 Living in water versus air

BOX 2.1 Passive diffusion of carbon dioxide in the boundary layer in air and in water

2.4 Light interception and photosynthesis

BOX 2.2 Absorption of light by chloroplasts

BOX 2.3 Formulas for the effective light absorption cross section of some geometric objects

BOX 2.4 Modeling light interception in canopies

2.5 Phototropism

2.6 Mechanoperception

2.7 Thigmomorphogenesis

2.8 Gravitropism

2.9 Root growth, root anchorage, and soil properties

CHAPTER 3. Plant Water Relations

3.1 The roles of water acquisition and conservation

3.2 Some physical properties of water

3.3 Vapor pressure and Raoult’s law

3.4 Chemical potential and osmotic pressure

3.5 Water potential

3.6 Turgor pressure and the volumetric elastic modulus

3.7 Flow through tubes and the Hagen-Poiseuille equation

3.8 The cohesion-tension theory and the ascent of water

3.9 Phloem and phloem loading

CHAPTER 4. The Mechanical Behavior of Materials

4.1 Types of forces and their components

4.2 Strains

4.3 Different responses to applied forces

4.4 A note of caution about normal stresses and strains

4.5 Extension to three dimensions

4.6 Poisson's ratios

BOX 4.1 Poisson’s ratio for an incompressible fluid

BOX 4.2 Poisson’s ratio for a cell

4.7 Isotropic and anisotropic materials

4.8 Shear stresses and strains

4.9 Interrelation between normal stresses and shear stresses

4.10 Nonlinear elastic behavior

4.11 Viscoelastic materials

4.12 Plastic deformation

4.13 Strength

4.14 Fracture mechanics

4.15 Toughness, work of fracture, and fracture toughness

4.16 Composite materials and structures

4.17 The Cook-Gordon mechanism

CHAPTER 5. The Effects of Geometry, Shape, and Size

5.1 Geometry and shape are not the same things

5.2 Pure bending

5.3 The second moment of area

5.4 Simple bending

BOX 5.1 Bending of slender cantilevers

BOX 5.2 Three-point-bending of slender beams

5.5 Bending and shearing

BOX 5.3 Bending and shearing of a cantilever

BOX 5.4 Bending and shearing of a simply supported beam

BOX 5.5 The influence of the microfibrillar angle on the stiffness of a cell

5.6 Fracture in bending

5.7 Torsion

5.8 Static loads

BOX 5.6 Comparison of forces on a tree trunk resulting from self-loading with those experienced in bending

5.9 The constant stress hypothesis

BOX 5.7 Predictions for the geometry of a tree trunk obeying the constant stress hypothesis

5.10 Euler buckling

5.11 Hollow stems and Brazier buckling

5.12 Dynamics, oscillation, and oscillation bending

BOX 5.8 Derivation of eigenfrequencies

CHAPTER 6. Fluid Mechanics

6.1 What are fluids ?

BOX 6.1 The Navier-Stokes equations

6.2 The Reynolds number

6.3 Flow and drag at small Reynolds numbers

BOX 6.2 Derivation of the Hagen-Poiseuille equation

6.4 Flow of ideal fluids

6.5 Boundary layers and flow of real fluids

BOX 6.3 Vorticity

6.6 Turbulent flow

BOX 6.4 Turbulent stresses and friction velocities

6.7 Drag in real fluids

6.8 Drag and flexibility

6.9 Vertical velocity profiles

6.10 Terminal settling velocity

6.11 Fluid dispersal of reproductive structures

CHAPTER 7. Plant Electrophysiology

7.1 The principle of electroneutrality

7.2 The Nernst-Planck equation

7.3 Membrane potentials

BOX 7.1 The Goldman equation

7.4 Ion channels and ion pumps

BOX 7.2 The Ussing-Teorell equation

7.5 Electrical currents and gravisensitivity

7.6 Action potentials

7.7 Electrical signaling in plants

CHAPTER 8. A Synthesis: The Properties of Selected Plant Materials, Cells, and Tissues

8.1 The plant cuticle

8.2 A brief introduction to the primary cell wall

BOX 8.1 Cell wall stress and expansion resulting from turgor

8.3 The plasmalemma and cell wall deposition

8.4 The epidermis and the tissue tension hypothesis

8.5 Hydrostatic tissues

BOX 8.2 Stresses in thick-walled cylinders

BOX 8.3 Compression of spherical turgid cells

8.6 Nonhydrostatic cells and tissues

8.7 Cellular solids

8.8 Tissue stresses and growth stresses

8.9 Secondary growth and reaction wood

8.10 Wood as an engineering material

CHAPTER 9. Experimental Tools

9.1 Anatomical methods on a microscale

9.2 Mechanical measuring techniques on a macroscale

9.3 Mechanical measuring techniques on a microscale

9.4 Scholander pressure chamber

9.5 Pressure probe

9.6 Recording of electric potentials and electrical currents

9.7 Patch clamp techniques

9.8 Biomimetics

BOX 9.1 An example of applied biomechanics: Tree risk assessment

CHAPTER 10. Theoretical Tools

10.1 Modeling

10.2 Morphology: The problematic nature of structure-function relationships

10.3 Theoretical morphology, optimization, and adaptation

10.4 Size, proportion, and allometry

BOX 10.1 Comparison of regression parameters

10.5 Finite element methods (FEM)

10.6 Optimization techniques

BOX 10.2 Optimal allocation of biological resources

BOX 10.3 Lagrange multipliers and Murray’s law

Glossary

Author index

Subject index

**Biological Sciences: **
Biology--Systematics |
Botany |
Ecology

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