The real strength of the book is the introduction of basic physical principles that are particularly relevant to biology excluding all quantum mechanical ones. The examples are taken chiefly from molecular and cellular biology, with rare examples from the world larger than the cell. In this he succeeds. In the end, the student will not have an understanding of modern experimental biology, but will have seen physics applied to basic biological elements DNA, proteins, lipids , and will have a feel for how physical forces dictate constraints on biological systems, and how biological systems use physics to get things done.
Students with a primary interest in physics will find this book a natural entry into biology.
Students with a primary interest in biology will learn how biological phenomena can be approached quantitatively. By stimulating student interest, integrated science texts like this one promote a long-term future filled with important developments in quantitative, theory-based biology. Just wondering if anyone has actually used this text in the classroom. For what level of students? And how did it work out? About Archive Contact. This motion is called shear.
The force f will be proportional to the area A of each plate. It will increase with increasingspeed v0, but decrease as we increase the plate separation.
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Equation 5. Theminus sign reminds us that the drag force opposes the imposed motion. You can verify that theunits work out in Equation 5. Low Reynolds number [[Student version, December 8, ]] Table 5. Equivalently, we can say that:a. We found a criterion for making this distinction in a given situationusing dimensional analysis. Table 5. In water, on the other hand, even a millinewtonpush puts us well into the regime dominated by inertia, not friction; indeed turbulent motion thenensues.
Life in the slow lane: the low Reynolds-number world [[Student version, December 8, ]]Chapter 10 that the typical scale of forces inside cells is more like a thousand times smaller, thepiconewton range. Friction rules the world of the cell. A large object—even a battleship—willmove in the friction-dominated regime, if we push on it with less than a nanonewton of force. Similarly, macroscopic experiments, like the one shown in Figure 5. T2 Section 5. Such arguments generallystrike students as dangerously sloppy.
Indeed, when faced with an unfamiliar situation a physicalscientist begins with dimensional arguments to raise certain expectations, but then proceeds tojustify those expectations with more detailed analysis. Low Reynolds number [[Student version, December 8, ]] Figure 5. The black area below the sphere is just its shadow. If the sphere were a single-cell organism, a food particle located in its path would simply get carried around itwithout ever encountering the cell at all.
Putting 2We are still dropping numerical factors to get an estimate; really the area is 6 2. Also, Equation 5. Ina series of careful experiments in the s, O. Compare the external force needed to anchor the obstruction in place to the viscous critical force. Solution: At low Reynolds number the inertial term is negligible, so fext is essen- tially equal to the frictional force Equation 5.
Your Turn 5dSuppose that the Reynolds number is big, R 1. Compare the external force needed to anchorthe obstruction in place to the viscous critical force. As always, we need to make some estimates. Thus each must exert on its neighbor above the same forceexerted on it by its neighbor below, or dvz x must be a constant, independent of x. A function dxwith constant derivative must be a linear function.
Thismotion is what stretches out an initially spherical blob of ink Figure 5. A second example may reinforce the point. Physically, xr describes a process where your. Life in the slow lane: the low Reynolds-number world [[Student version, December 8, ]]car is initially rolling backwards, then hits a wall behind you and stops.
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Once again your headrestpushes forward on your head. In other words,In Newtonian physics the time-reversed process is a solution to the equations 5. Certainly a pebble in molassesnever falls upward, regardless what starting velocity we choose! Instead, to get the time-reversedmotion we must apply a force that is time reversed and opposite in direction to the original.
The failure of time-reversal invariance is simply a signal that something irreversible is happeningin frictional motion. Phrased this way, the conclusion is not surprising: We already knew thatfriction is the one-way dissipation, or degradation, of ordered motion into disordered motion.
Oursimple model for friction in Section 4. Here is another example of the same analysis. Take a moment tovisualize c2 and c3 for the example shown in Figure 4.
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Supposewe put an elastic solid, like rubber, between the plates in Figure 5. Biological applications [[Student version, December 8, ]] abcFigure 5. Three swimmers.
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These results may be amusing to us, but they are matters of life and death to microorganisms. It can only do so bychanging the shape of its body in some periodic way. A more detailed examplecan help make this clearer.
We know that in low Reynolds-number motion, moving. Life in the slow lane: the low Reynolds-number world [[Student version, December 8, ]]Figure 5. A hypothetical microscopic swimmer trying to make progress by cycling between forwardand backward strokes of its paddles. On the second stroke the paddles move forward at relativespeed v , propelling the body backward at speed u. Then the cycle repeats. Then it pushes its paddles backward towardnegative x relative to its body at a relative speed v for a time t.
The cycle repeats. Example a. Repeat a,b for the second return stroke. Your friend proposes to choose v and v to optimize this process. How do you advise him? Solution: a. The answers to b and c always cancel, regardless of what we take for v and v. But such a recovery stroke.
Biological applications [[Student version, December 8, ]] 3 5 10 9 effective stroke recovery strokeFigure 5. The ciliary cycle. Whatother options does a microorganism have? The required motion must be periodic, so that it canbe repeated. Here are twoexamples. The motion in Figure 5.
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Indeed thismotion is periodic but not reciprocal. Duringthe power stroke left panel the entire cilium moves perpendicular to its axis, whereas during therecovery stroke right panel most of it is moving nearly parallel to its axis. In this case Figure 5. The bacterium E.
A thin rod is dragged at low Reynolds number with velocity v.