Landau-Lifshitz theory

Lagrange Multiplier Method for programming problems, 289 for weapon allocation, 291 Lamb and Rutherford, 641 Lamb shift, 486,641 Lanczos form, 73 Landau, L. D., 726,759, 768 Landau-Lifshitz theory applied to magnetic structure, 762 Large numbers, weak law of, 199 Law of large numbers, weak, 199 Lawson, J. L., 170,176 Le Cone, Y., 726... 

Refinements in the theory of interparticle long-range van der Waals forces (the Landau-Lifshitz theory) are within reach. New techniques are now available for measuring the complex dielectric constants of various media required for the implementation of that theory. 

Landau-Ginzbuig coefficients 282 Landau-Ginzburg Hamiltonian, critical 303 Landau-Khalatnikov mechanism 564 Landau-Lifshitz theory, phase transitions 366 Landau-Peierls instabilities 285, 647 Langmuir-Blodgett film, atomistic simulations 85 Laplace equation 445... 

L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Pergamon Press, New York, 1986. 

We will present the equation of motion for a classical spin (the magnetic moment of a ferromagnetic single-domain particle) in the context of the theory of stochastic processes. The basic Langevin equation is the stochastic Landau-Lifshitz(-Gilbert) equation [5,45]. More details on this subject and various techniques to solve this equation can be found in the reviews by Coffey et al. [46] and Garcia-Palacios [8]. 

The Maxwell theory of X-ray scattering by stable systems, both solids and liquids, is described in many textbooks. A simple and compact presentation is given in Chapter 15 of the Landau-Lifshitz volume. Electrodynamics of Continuous Media [20]. The incident electric and magnetic X-ray fields are plane waves... 

LD Landau, EM Lifshitz. Theory of Elasticity. 3rd ed. Oxford Pergamon, 1986. 

Values of e, n and ve and Hamaker constants for two identical types of a material in a vacuum, which are calculated from Equation (567) by taking e3 = 1 and 3 = 1, are given in Table 7.1. Unfortunately, the lack of material constants, such as the dielectric constant, as a function of frequency for most of the substances, and also the complexity of the derived formulae have hampered the general use of the Lifshitz model. However, Lifshitz theory made possible the advent of the first theories on the stability of hydrophobic colloids as a balance between London attraction and electrical double-layer repulsion. Later, these theories were further elaborated by Derjaguin and Landau, and independently by Verwey and Overbeek. The general theory of colloidal stability (which is beyond the scope of this book) is based on Lifshitz theory and has become known as the DLVO theory, by combining the initials of these four authors. 

Although originally designed for astrophysical problems [86], as shown in [120], SPH can also be used for modeling polymers in the macroscale. However, smoothed particle hydrodynamics does not include thermal fluctuations in the form of a random stress tensor and heat flux as in the Landau and Lifshitz theory of hydrodynamic fluctuations. Therefore, the validity of SPH to the study of complex fluids is problematic at scales where thermal fluctuations are important. 

The second volume of the Landau-Lifshitz series on theoretical physics continues directly after volume I and covers the classical theory of fields. It starts with an introduction of Einstein s principle of relativity and a discussion of the special theory of relativity for mechanics. It follows a rather complete presentation of classical electrodynamics including radiation phenomena and scattering of waves of different energy. It concludes with an introduction of gravitational fields, the theory of general relativity and classical relativistic cosmology. 

Elastic models lead to p=3 if the stress is uniformly distributed through the thickness of a bent sheet e.g. L. D. Landau and E. M. Lifshitz, "Theory of Elasticity," Pergamon, New York (1970) S. T. Milner and T. A. Witten, M. E. Cates, Europhysics, Lett. 5, 413... 

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