Книги. Художественная литература. Учебники и пособия.

High Quality Content by WIKIPEDIA articles! In quantum mechanics, a probability amplitude is a complex number whose absolute value squared represents a probability or probability density. For example, the values taken by a normalised wave function ? are amplitudes, since |?(x)|2 gives the probability density at position x. Probability amplitudes may also correspond to probabilities of discrete outcomes. The principal use of probability amplitudes is as the physical meaning of the wavefunction, a link first proposed by Max Born and a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the wave function were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation was offered. Born was awarded half of the 1954 Nobel Prize in physics for this understanding, though it was vigorously contested at the time by the original physicists working on the theory, such as...

Adelina Georgescu, Lidia Palese

This is a comprehensive and self-contained introduction to the mathematical problems of thermal convection. The book delineates the main ideas leading to the authors' variant of the energy method. These can be also applied to other variants of the energy method. The importance of the book lies in its focussing on the best concrete results known in the domain of fluid flows stability and in the systematic treatment of mathematical instruments used in order to reach them.

J. B. Kuipers

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Brian Greene

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High Quality Content by WIKIPEDIA articles! In mathematical physics, spacetime algebra is a name for the Clifford algebra C?1,3(R), which can be particularly closely associated with the geometry of special relativity and relativistic spacetime. It is a linear algebra allowing not just vectors, but also directed quantities associated with particular planes (for example: areas, or rotations) or associated with particular (hyper-)volumes to be combined, as well as rotated, reflected, or Lorentz boosted. It is also the natural parent algebra of spinors in special relativity. These properties allow many of the most important equations in physics to be expressed in particularly simple forms; and can be very helpful towards a more geometrical understanding of their meanings.

Ubiquitous and fundamental in cell mechanics, multiscale problems can arise in the growth of tumors, embryogenesis, tissue engineering, and more. Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling brings together new insight and research on mechanical, mathematical, physical, and biological approaches for simulating the behavior of cells, specifically tumor cells. In the first part of the text, the book discusses the powerful tool of microrheology for investigating cell mechanical properties, multiphysics and multiscale approaches for studying intracellular mechanisms in cell motility, and the role of subcellular effects involving certain genes for inducing cell motility in cancer. Focusing on models based on physical, mathematical, and computational approaches, the second section develops tools for describing the complex interplay of cell adhesion molecules and the dynamic evolution of the cell cytoskeleton. The third part explores cell interactions with the...

Sergey V. Simonenko

A new approach to the theory of the small-scale dissipative turbulence based on non-equilibrium thermodynamics, continuum-mechanics and the statistical physics is developed in the monograph. The classical expression for the macroscopic kinetic energy of a small fluid particle in classical non-equilibrium thermodynamics is generalized by taking into account the local velocity shear related with the rate of strain tensor. The closure relation for the three-dimensional isotropic homogeneous small-scale dissipative turbulence (in an incompressible viscous Newtonian fluid) is founded by combining the classical statistical approaches, the conception of the statistical ensemble and the classical formulation of the law of large numbers. The significance of the new approach is evaluated for laboratory and oceanic stratified turbulence. The practical application of the new approach is shown in physical oceanography. For specialists in non-equilibrium thermodynamics, continuum mechanics,...

Maria Tomas-Rodriguez, Stephen P. Banks

Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those a?? well-known a?? based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Chitrlada T. Settakorn

This book is intended especially for students and researchers working with generation, interpretation and applications of THz transition radiation. It concentrates in much detail on theoretical and experimental discussions of coherent THz femtosecond transition radiation from ultrashort electron pulses and will serve as a guide for experimental design to generate and characterize such radiation with detailed interpretations. Experimental results of non-destructive diffraction radiation are also discussed in much detail. In one of its applications, coherent transition radiation is being used for longitudinal beam diagnostics, especially bunch length measurement with femtosecond pulse resolution. Complete performance, analyses and limitations of bunch length measurements via the autocorrelation technique will be presented in this book. The feature of femtosecond THz pulse is exploited in an example application to material science measuring the complex dielectric constant of materials...

Bob Schutz, George H. Born, Byron Tapley

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