tailieunhanh - The Self-Made Tapestry Phần 5

Nếu chúng ta nghĩ về một tương tự mô hình trong đó áp lực tương đương với chiều cao của một ngọn đồi và chuyển động của bong bóng không khí tương đương với chuyển động của quả bóng, quả bóng tăng tốc nhanh hơn xuống đồi dốc hơn từ isin khác,là gradient để xác định tỷ lệ tạm ứng. | Page 11 highest to the value in the bulk of the oil. If we think of a model analogy in which the pressure is equivalent to the height of a hill and the motion of the air bubble is equivalent to the motion of a ball the ball accelerates more rapidly down the hill the steeper it isin other words it is the gradient that determines the rate of advance. Saffman and Taylor pointed out that the gradient in pressure around a bulge at the air oil interface gets steeper as the bulge gets sharper. This sets up a self-amplifying process in which a small initial bulge begins to move faster than the interface to either side. The sharper and longer the finger gets the steeper the pressure gradient at its tip and so the more rapidly it grows Fig. . Fig. The Saffman-Taylor instability. As a bulge develops at the advancing fluid front the pressure gradient at the bulge tip is enhanced and so the tip advances more rapidly. Contours of constant pressureisobars like those in weather mapsare shown as dashed lines. This amplifies small bulges into sharp fingers. Compare this to the growth instability in DLA Fig. . This instability is called the SaffmanTaylor instability. In 1984 Australian physicist Lincoln Paterson pointed out that the equations that describe it are analogous to those that underlie the DLA instability described by Witten and Sander. So it is entirely to be expected that viscous fingering and DLA produce the same kind of fractal branching networks. Both are examples of so-called Laplacian growth which can be described by a set of equations derived from the work of the eighteenth-century French scientist Pierre Laplace. Within these deceptively simple equations are the ingredients for growth instabilities that lead to branching. But tenuous fractal patterns directly comparable to those of DLA occur in viscous fingering only under rather unusual conditions. More commonly one sees a subtlely altered kind of branching structure the basic pattern or backbone of

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