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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.

A symbiotic relationship between botany and the fields of physics, mathematics, engineering, and chemistry continues today, as is revealed in 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.  


448 pages | 44 halftones, 40 line drawings, 9 tables | 6 x 9 | © 2012

Biological Sciences: Biology--Systematics, Botany, Ecology


“[A]n interesting interdisciplinary glimpse into the physics of plant biology. . . . A useful resource for advanced courses in botany, plant physiology, and biophysics. Recommended.”

J. Z. Kiss, Miami University | Choice

“There is no better way to learn about plants than studying physics and to learn physics than studying plants. This book does just so. In a comprehensive but not overwhelming manner, the authors provide an overview of carefully selected topics that beautifully link descriptions of plant physiological and cellular activity with explanations of the physical forces that shape plant structure and function. . . . I enjoyed reading this volume and would recommend it as a valuable addition to the bookshelves in all plant biology or physics graduate rooms and for all plant biology or physics teachers.”

Maciej Zwieniecki, Harvard University | Quarterly Review of Biology

“Brilliant. . . . This is truly a lovely book.”

Plant Science Bulletin

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

R. S. Shorter, Winchester College | Contemporary Physics

“A significant addition to the literature on plant structure. Plant Physics presents a comprehensive overview of the physics relevant to the structural economy of land plants. . . . For the plant biologist, this book will be an invaluable reference for many years. For the physicist, the attraction of this book may be the breadth of topics covered and the implication that physics lies at the very heart of plant developmental biology.”

Philip Lintilhac, University of Vermont, Burlington | BioScience

“Here’s the physical world of plants in all its splendor—and multidimensionality—brought to bear on the rich diversity of both extant and extinct forms. Niklas and Spatz’s theme, which deserves attention, is that since plants (and animals, of course) cannot change physics, physical laws and processes must bear strongly on the course of their evolution.”

Steven Vogel, Duke University

“Karl J. Niklas and Hanns-Christof Spatz have written a remarkable book, unique in the field of biomechanics. Starting from basic physical principles, it explains a wide range of phenomena in plants, from fluid transport to the dispersal of seeds in air and water to structural behavior. The experimental and theoretical tools described provide a useful primer. A valuable reference for researchers interested in how plants work from a physical perspective.”

Lorna Gibson, Massachusetts Institute of Technology

Table of Contents

Recommended Reading
Frequently Used Symbols

CHAPTER 1. An Introduction to Some Basic Concepts
 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

Author index
Subject index

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