This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the...
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the ...
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author's extension of the theory will...
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theor...
This monograph provides an account of thermal convection with a focus on Cattaneo's heat flux equation. Various applications of the equation are analyzed, such as those pertaining to nanoscale mechanics, nuclear engineering, the treatment of various diseases, and more. The influence it has had on problems in the field of thermal convection is highlighted as well. Several other important topics are incorporated, including:
Guyer-Krumhansl terms
Kelvin-Voigt fluid theory
Navier-Stokes theory
Higher gradient fluid theories
Thermal Convection...
This monograph provides an account of thermal convection with a focus on Cattaneo's heat flux equation. Various applications of the equation are an...
This volume presents recent advances in the field of dynamic equations on time scales and functional differential equations, with a focus on how these topics can be used to describe phenomena in continuum mechanics. Chapters investigate important aspects of these equations, such as asymptotic behavior and the qualitative properties of their solutions. Specific topics covered include:
Ulam stability for dynamic equations
Generalized ordinary differential equations
Singular control systems on time scales
Bresse...
This volume presents recent advances in the field of dynamic equations on time scales and functional differential equations, with a focus on how th...
This volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more. Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats, non-Newtonian...
This volume explores the application of topological techniques in the study of delay and ordinary differential equations with a particular focus on...
