## Statistical mechanics: fundamentals and modern applicationsThis book examines the latest developments in statistical mechanics, a branch of physical chemistry and physics that uses statistical techniques to predict the properties and the behavior of chemical and physical systems. It begins with a review of some of the essential concepts and then discusses recent developments in both equilibrium and nonequilibrium statistical mechanics. It covers liquids, phase transitions, renormalization theory, Monte Carlo techniques, and chaos. |

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Page 343

the curves are composed of vanishingly small line segments that meet at sharp

angles. Since the

**Fractal**curves, on the other hand, are continuous but nondifferentiable, becausethe curves are composed of vanishingly small line segments that meet at sharp

angles. Since the

**fractal**curves are not differentiable, they have an infinite length.Page 344

where D is called the

defined for a self-similar object. Solving for D, D = -lnN/lnr (13.11) An example of

a

where D is called the

**fractal**dimension. Actually, what we shall refer to as the**fractal**dimension is more properly called the similarity dimension, since it isdefined for a self-similar object. Solving for D, D = -lnN/lnr (13.11) An example of

a

**fractal**...Page 345

For each application of the generator, r = I andiV = 3, which gives a

dimension of D — In 3/ In 2 = 1.58. 13.4.3

126 Starting from an ordered state at a single site with a value 1 , cellular

automaton 126 ...

For each application of the generator, r = I andiV = 3, which gives a

**fractal**dimension of D — In 3/ In 2 = 1.58. 13.4.3

**Fractal**Nature of Cellular Automaton126 Starting from an ordered state at a single site with a value 1 , cellular

automaton 126 ...

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### Contents

Classical Statistical Mechanics | 3 |

Quantum Statistical Mechanics | 45 |

Phase Transitions and Critical Phenomena | 83 |

Copyright | |

14 other sections not shown

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attractor automata average behavior bifurcation Boltzmann Boltzmann equation Brownian motion Brownian particle BZ reaction calculate called canonical ensemble cell cellular automaton chaos Chapter coefficient collisions configuration consider coordinates correlation functions coupling constants critical exponents critical point defined depends derivation dimension discussed distribution function dynamics eigenvalues entropy equilibrium evaluated example ferromagnetic fixed point fluctuations fluid FORTRAN FORTRAN program fractal free energy frequency Gaussian Hamiltonian initial integral interactions Ising model iterations Kramers Langevin equation lattice limit cycle linear magnetization Markovian matrix method microcanonical ensemble microstates molecular nonequilibrium nonlinear number of particles obtained one-dimensional order parameter oscillations partition function Pathria phase space phase transition polymer potential power spectrum probability density problem protein quantities quantum mechanics RANDOM NUMBER random walk scaling Section shown in Figure simulation solution spin glass statistical mechanics steps stochastic temperature theorem thermodynamic limit total number values vector velocity zero