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  • 1
    Electronic Resource
    Electronic Resource
    Macroscopic thermodynamics of flowing polymeric liquids (1999)
    Springer
    Rheologica acta 38 (1999), S. 117-136 
    Details
    ISSN: 1435-1528
    Keywords: Key words Non-isothermal flows ; Polymeric liquids ; Thermodynamics ; Non-Newtonian fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The thermodynamics and mechanics of non-isothermal polymeric fluids are examined within the auspices of a new methodology wherein the laws of physics and principles of mechanics which are applicable to these thermodynamic systems are imbedded in a definite mathematical structure of a general, abstract equation. Such a concept allows new insight to be obtained concerning some aspects of non-isothermal flows of polymeric fluids, and permits a consistent expression and interpretation of other thermodynamic theories for these systems which have been developed over the past forty years. A major portion of this article is devoted to demonstrating the above statements, and in so doing some common misconceptions occurring in a significant fraction of the literature regarding this subject are exposed. The definite mathematical structure of the new methodology permits the thermodynamically consistent generalization of isothermal, incompressible models of polymeric fluids to non-isothermal, compressible conditions. Doing thus reproduces, corrects, and extends non-isothermal models which have been developed over the years, and also allows for simpler (but equivalent) representations of these models in terms of alternate variables with a clearer connection to the microstructure of the material than the stress tensor and heat flux vector fields. Furthermore, a generalization of the GENERIC structure is proposed that accommodates interactions between phenomena of differing parities, which impose antisymmetry upon the corresponding elements of the dissipative operator matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003970050162
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  • 2
    Electronic Resource
    Electronic Resource
    Rotational Motion and Poisson Bracket Structures in Rigid Particle Systems and Anisotropic Fluid Theory (1998)
    Springer
    Open systems & information dynamics 5 (1998), S. 333-368 
    Details
    ISSN: 1573-1324
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Natural Sciences in General
    Notes: Abstract We explore the origins of rotational motion in anisotropic fluid theories from the most fundamental perspectives possible: collections of discrete entities or continuous spectra of fluid particles which are allowed to translate and rotate simultaneously. In either case, the starting point of our analysis is the principle of least action applied to rigid body systems involving both translation and rotation. Our methods of analyzing this problem are both very old and very recent, and we hope that the net result of these methods is an injection of much originality into an old problem. Hamiltonian mechanics of a system of discrete particles is considered where explicit accounting is made of both translational and rotational particle motion. The extended Poisson bracket is written down in terms of appropriate generalized coordinates and the Hamiltonian of the system. A similar treatment in terms of quasi-coordinates is also presented. An alternative formulation in terms of two orthogonal unit vectors is offered which simplifies the mathematical description of the system by working in an inertial reference frame with constant, diagonal inertia tensors. This methodology is transferred to a continuum material description in terms of functional relationships and Volterra differentiation. An analogous continuum bracket is derived, and ultimately transferred to a spatial description, along with the Hamiltonian. This results in a derivation of the most general form of the ideal anisotropic fluid equations in terms of the appropriate variables, an important subcase of which is the Leslie-Ericksen theory of liquid crystals. It extends and also provides insight into the molecular origins of the various constitutive relationships of continuum anisotropic fluid theories (such as the inertia tensor, body force, body couple, etc.). Our motivation is to provide, based on the Poisson bracket structure for all different descriptions of rigid particle rotation, an a priori derivation of the Poisson bracket structure corresponding to the rotational motion described in continuum anisotropic fluid theories which also leads to their consistent generalization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009691800395
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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