Definitions of standard stress and standard heat flux, in simple bodies, treated according to Mach and Painlevé
On tensor functions whose gradients have some skew-symmetries
Let be a real inner product space of any dimension; and let be a -map relating any two tensor spaces on . We study the consequences imposed on the form of this function by the condition that its gradient should be skew-symmetric with respect to some pairs of indexes. Any such a condition is written as a system of linear partial differential equations, with constant coefficients, which is symmetric with respect to certain couples of independent variables. The solutions of these systems appear...
A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 2. Alternative completion of Bressan's work, fit for extension to special relativity
The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- is suitable for extension to special relativity. The main reason of this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following [1], the notion of (physical) equivalence among affine inertial frames, and that of (physical isotropy of these frames are introduced; it is shown that...
A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames
The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...
A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames
The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...
A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 2. Alternative completion of Bressan's work, fit for extension to special relativity
The work [3] of axiomatization of various classical theories on continuous bodies from the Mach-Painlevè point of view, is completed here in a way which -unlike [4]- is suitable for extension to special relativity. The main reason of this is the fact that gravitation can be excluded in all the theories on continuous bodies considered here. Following [1], the notion of (physical) equivalence among affine inertial frames, and that of (physical isotropy of these frames are introduced; it is shown that...
General and physically privileged solutions to certain symmetric systems of linear P.D.E.s with tensor functionals as unknowns
We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere dense...
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