Scalar, vectorial and tensorial damage parameters from the mesoscopic background

In the mesoscopic theory a distribution of different crack sizes and crack orientations is introduced. A scalar damage parameter, a second order damage tensor and a vectorial damage parameter are defined in terms of this distribution function. As an example of a constitutive quantity the free energy density is given as a function of the damage tensor. This equation is reduced in the uniaxial case to a function of the damage vector and in case of a special geometry to a function of the scalar damage parameter.Comment: 14 pages, 2 figure

A mesoscopic approach to diffusion phenomena in mixtures

The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion differential equations for the diffusion fluxes, and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in Extended Thermodynamics. The resulting evolution equation for the diffusion flux generalizes the Fick's law

Mesoscopic continuum mechanics applied to liquid crystals

Beyond the usual 5-field theory (basic fields: mass density, velocity, internal energy), additional variables are needed for the unique description of complex media. Beside the conventional method of introducing additional fields by their balances, an other procedure, the mesoscopic theory, is here discussed and applied to liquid crystals

Variational Principles in Thermodynamics

Instead of equations of motion, variational principles are often used for describing the dynamical behavior of a system. If the equations of motion are variational self-adjoint, the variational principle is equivalent to the equations of motion, because those are given by the Euler-Lagrange equations which belong to the variational principle. If the equations of motion are not variational self-adjoint -as it is the general case in thermodynamics- procedures are discussed to obtain also in these cases a variational problem. Because of lack of variational self-adjointness these variational problems cannot be true ones, they are non-Hamiltonian. By presupposing suflicient conditions an evolution criterion can be derived from the Second Law which results in a Hamiltonian variational principle, also in thermodynamics

Application of the Mesoscopic Theory to Dipolar Media

Mesoscopic continuum theory is a way to deal with complex materials, i.e. materials with an internal structure, which can change under the action of external elds, within continuum theory. In the mesoscopic theory eld quantities are introduced, which depend not only on position and time, but also on an additional, so called mesoscopic variable. In our case this additional variable is the orientation of a dipole. The orientation distribution function (ODF) gives the fraction of dipoles of a particular orientation. The magnetization is proportional to the rst moment of the ODF. Balance equations for the mesoscopic elds, and an equation of motion for the distribution function have been derived in the general case. With some additional assumptions these equations are used here to derive a relaxation equation for the magnetization. The linear limit case of this relaxation equation is the well known DEBYE equation

Evolution of mitochondrial relationships and biogeography of Palearctic green toads (Bufo viridis subgroup) with insights in their genomic plasticity.

Taxa involving three bisexually reproducing ploidy levels make green toads a unique amphibian system. We put a cytogenetic dataset from Central Asia in a molecular framework and apply phylogenetic and demographic methods to data from the entire Palearctic range. We study the mitochondrial relationships of diploids to infer their phylogeography and the maternal ancestry of polyploids. Control regions (and tRNAs between ND1 and ND2 in representatives) characterize a deeply branched assemblage of twelve haplotype groups, diverged since the Lower Miocene. Polyploidy has evolved several times: Central Asian tetraploids (B. oblongus, B. pewzowi) have at least two maternal origins. Intriguingly, the mitochondrial ancestor of morphologically distinctive, sexually reproducing triploid taxa (B. pseudoraddei) from Karakoram and Hindukush represents a different lineage. We report another potential case of bisexual triploid toads (B. zugmayeri). Identical d-loops in diploids and tetraploids from Iran and Turkmenistan, which differ in morphology, karyotypes and calls, suggest multiple origins and retained polymorphism and/or hybridization. A similar system involves diploids, triploids and tetraploids from Kyrgyzstan and Kazakhstan where green toads exemplify vertebrate genomic plasticity. A new form from Sicily and its African sister species (B. boulengeri) allow internal calibration and divergence time estimates for major clades. The subgroup may have originated in Eurasia rather than Africa since the earliest diverged lineages (B. latastii, B. surdus) and earliest fossils occur in Asia. We delineate ranges, contact and hybrid zones. Phylogeography, including one of the first non-avian datasets from Central Asian high mountains, reflects Quaternary climate and glaciation

Bosonic field equations from an exact uncertainty principle

A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of the field momentum density, of a strength determined solely by the field uncertainty, is shown to lead to a unique modification of the ensemble Hamiltonian. The modified equations of motion are equivalent to the quantum equations for a bosonic field, and thus this exact uncertainty principle provides a new approach to deriving and interpreting the properties of quantum ensembles. The examples of electromagnetic and gravitational fields are discussed. In the latter case the exact uncertainty approach specifies a unique operator ordering for the Wheeler-DeWitt and Ashtekar-Wheeler-DeWitt equations.Comment: 24 pages, extended version of part (B) of hep-th/0206235, to appear in J. Phys.