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Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of a surface by its mean curvature. This mathematical description encompasses, among other subtleties, those of changing geometries and instantaneous mass losses.Originally published in 1978.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Geometric measure theory. --- Surfaces. --- Curvature. --- Measure theory --- Calculus --- Curves --- Surfaces --- Curved surfaces --- Geometry --- Shapes --- Affine transformation. --- Approximation. --- Asymptote. --- Barrier function. --- Besicovitch covering theorem. --- Big O notation. --- Bounded set (topological vector space). --- Boundedness. --- Calculation. --- Cauchy–Schwarz inequality. --- Characteristic function (probability theory). --- Compactness theorem. --- Completing the square. --- Concave function. --- Convex set. --- Convolution. --- Crystal structure. --- Curve. --- Derivative. --- Diameter. --- Differentiable function. --- Differentiable manifold. --- Differential geometry. --- Dimension. --- Domain of a function. --- Dyadic rational. --- Equivalence relation. --- Estimation. --- Euclidean space. --- Existential quantification. --- Exterior (topology). --- First variation. --- Gaussian curvature. --- Geometry. --- Grain boundary. --- Graph of a function. --- Grassmannian. --- Harmonic function. --- Hausdorff measure. --- Heat equation. --- Heat kernel. --- Heat transfer. --- Homotopy. --- Hypersurface. --- Hölder's inequality. --- Infimum and supremum. --- Initial condition. --- Lebesgue measure. --- Lebesgue point. --- Linear space (geometry). --- Lipschitz continuity. --- Mean curvature. --- Melting point. --- Microstructure. --- Monotonic function. --- Natural number. --- Nonparametric statistics. --- Order of integration (calculus). --- Order of integration. --- Order of magnitude. --- Parabolic partial differential equation. --- Paraboloid. --- Partial differential equation. --- Permutation. --- Perpendicular. --- Pointwise. --- Probability. --- Quantity. --- Quotient space (topology). --- Radon measure. --- Regularity theorem. --- Retract. --- Rewriting. --- Riemannian manifold. --- Right angle. --- Second derivative. --- Sectional curvature. --- Semi-continuity. --- Smoothness. --- Subsequence. --- Subset. --- Support (mathematics). --- Tangent space. --- Taylor's theorem. --- Theorem. --- Theory. --- Topology. --- Total curvature. --- Translational symmetry. --- Uniform boundedness. --- Unit circle. --- Unit vector. --- Upper and lower bounds. --- Variable (mathematics). --- Varifold. --- Vector field. --- Weight function. --- Without loss of generality.

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"This book aims to give the reader the theoretical and numerical tools to understand, explain, calculate and predict the often non intuitive, observed behaviour of droplets in microsystems. After a chapter dedicated to the general theory of wetting, the book successively. Presents the theory of 3D liquid interfaces, gives the formulas for volume and surface of sessile and pancake droplets, analyses the behaviour of sessile droplets, analyses the behaviour of droplets between tapered plates and in wedges, presents the behaviour of droplets in microchannels investigates the effect of capillarity with the analysis of capillary rise, treats the onset of spontaneous capillary flow in open microfluidic systems, analyses the interaction between droplets, like engulfment, presents the theory and application of electrowetting"--

Microdroplets. --- Microfluidics. --- Capillarity. --- Capillarity --- Microdroplets --- Microfluidics --- Fluidics --- Nanofluids --- Drops --- Matter --- Physics --- Permeability --- Surface chemistry --- Surface tension --- Properties

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Minimal surfaces. --- Plateau's problem. --- Differential topology. --- Differential topology --- Minimal surfaces --- Plateau's problem --- Minimal surface problem --- Plateau problem --- Problem of Plateau --- Surfaces, Minimal --- Maxima and minima --- Geometry, Differential --- Topology