Symmetry classes for even-order tensors

The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, piezoelectricity, flexoelectricity, and strain-gradient elasticity. All the aforementioned problems were treated by the same computational method. Although being effective, this method suffers the drawback not to provide general results. And, furthermore, its complexity increases with the tensorial order. In the present contribution, we provide general theorems that directly give the sought results for any even-order constitutive tensor. As an illustration of this method, and for the first time, the symmetry classes of all even-order tensors of Mindlin second strain-gradient elasticity are provided.Comment: Mathematics and Mechanics of Complex Systems (2013) (Accepted

Large Scale Baryon Isocurvature Inhomogeneities

Big bang nucleosynthesis constraints on baryon isocurvature perturbations are determined. A simple model ignoring the effects of the scale of the perturbations is first reviewed. This model is then extended to test the claim that large amplitude perturbations will collapse, forming compact objects and preventing their baryons from contributing to the observed baryon density. It is found that baryon isocurvature perturbations are constrained to provide only a slight increase in the density of baryons in the universe over the standard homogeneous model. In particular it is found that models which rely on power laws and the random phase approximation for the power spectrum are incompatible with big bang nucleosynthesis unless an {\em ad hoc}, small scale cutoff is included.Comment: 11pages + 8figures, LaTeX (2.09), postscript figures available via anonymous ftp from oddjob.uchicago.edu:/ftp/ibbn/fig?.ps where ?=1-8 or via email from [email protected], Fermilab-Pub-94/???-A and UMN-TH-1307/9

Critical behavior of plastic depinning of vortex lattices in two dimensions: Molecular dynamics simulations

Using molecular dynamics simulations, we report a study of the dynamics of two-dimensional vortex lattices driven over a disordered medium. In strong disorder, when topological order is lost, we show that the depinning transition is analogous to a second order critical transition: the velocity-force response at the onset of motion is continuous and characterized by critical exponents. Combining studies at zero and nonzero temperature and using a scaling analysis, two critical expo- nents are evaluated. We find v\sim (F-F_c)^\beta with \beta=1.3\pm0.1 at T=0 and F>F_c, and v\sim T^{1/\delta} with \delta^{-1}=0.75\pm0.1 at F=F_c, where F_c is the critical driving force at which the lattice goes from a pinned state to a sliding one. Both critical exponents and the scaling function are found to exhibit universality with regard to the pinning strength and different disorder realizations. Furthermore, the dynamics is shown to be chaotic in the whole critical region.Comment: 8 pages, 6 figure

Primordial Nucleosynthesis and the Abundances of Beryllium and Boron

The ability to now make measurements of Be and B as well as put constraints on \lisix\ abundances in metal-poor stars has led to a detailed reexamination of Big Bang Nucleosynthesis in the A\groughly6 regime. The nuclear reaction network has been significantly expanded with many new rates added. It is demonstrated that although a number of $A>7$ reaction rates are poorly determined, even with extreme values chosen, the standard homogeneous model is unable to produce significant yields (Be/H and B/H $<10^{-17}$ when $A\le7$ abundances fit) above $A=7$ and the \liseven/\lisix\ ratio always exceeds 500. We also preliminarily explore inhomogeneous models, such as those inspired by a first order quark-hadron phase transition, where regions with high neutron/proton ratios can allow some leakage up to $A>7$. However models that fit the $A\le7$ abundances still seem to have difficulty in obtaining significant $A>7$ yields.Comment: Plain TeX, 28 pages, 8 figures (not included, but available from authors). UMN-TH-1020/9

The elastic depinning transition of vortex lattices in two dimensions

Large scale numerical simulations are used to study the elastic dynamics of two-dimensional vortex lattices driven on a disordered medium in the case of weak disorder. We investigate the so-called elastic depinning transition by decreasing the driving force from the elastic dynamical regime to the state pinned by the quenched disorder. Similarly to the plastic depinning transition, we find results compatible with a second order phase transition, although both depinning transitions are very different from many viewpoints. We evaluate three critical exponents of the elastic depinning transition. $\beta = 0.29 \pm 0.03$ is found for the velocity exponent at zero temperature, and from the velocity-temperature curves we extract the critical exponent $\delta^{-1} = 0.28 \pm 0.05$. Furthermore, in contrast with charge-density waves, a finite-size scaling analysis suggests the existence of a unique diverging length at the depinning threshold with an exponent $\nu= 1.04 \pm 0.04$, which controls the critical force distribution, the finite-size crossover force distribution and the intrinsic correlation length. Finally, a scaling relation is found between velocity and temperature with the $\beta$ and $\delta$ critical exponents both independent with regard to pinning strength and disorder realizations.Comment: 17 pages, 10 figure

Le centre d'apprentissage de langues: Représentations, motivations et réalités.

Au delà de son aspect matériel, la réalité d'un centre de langues est composée d'un 'espace' cognitif destiné à favoriser l'apprentissage. Les apprenants évoluent dans cet espace de manière plus ou moins autonome, le personnel du centre étant là pour les guider le cas échéant. Afin de trouver une organisation optimale, le personnel tente de prendre en compte les représentations et les motivations des étudiants, pour qui l'apprentissage dans un centre de langues est souvent une expérience nouvelle. Une évaluation du centre est nécessaire pour savoir comment ses ressources sont perçues et utilisées. Le dispositif mis en place peut ensuite être modifié pour favoriser l'émergence de stratégies propices à l'apprentissage. Nous présentons ici un exemple de cette réalité « interne » d'un centre de langues, où l'espace créé résulte de la rencontre entre réflexion didactique, supports matériels et comportements d'apprenants

Le centre d'apprentissage de langues: Représentations, motivations et réalités.

Au delà de son aspect matériel, la réalité d'un centre de langues est composée d'un 'espace' cognitif destiné à favoriser l'apprentissage. Les apprenants évoluent dans cet espace de manière plus ou moins autonome, le personnel du centre étant là pour les guider le cas échéant. Afin de trouver une organisation optimale, le personnel tente de prendre en compte les représentations et les motivations des étudiants, pour qui l'apprentissage dans un centre de langues est souvent une expérience nouvelle. Une évaluation du centre est nécessaire pour savoir comment ses ressources sont perçues et utilisées. Le dispositif mis en place peut ensuite être modifié pour favoriser l'émergence de stratégies propices à l'apprentissage. Nous présentons ici un exemple de cette réalité « interne » d'un centre de langues, où l'espace créé résulte de la rencontre entre réflexion didactique, supports matériels et comportements d'apprenants

Neutrino degeneracy and cosmological nucleosynthesis, revisited

A reexamination of the effects of non-zero degeneracies on Big Bang Nucleosynthesis is made. As previously noted, non-trivial alterations of the standard model conclusions can be induced only if excess lepton numbers L sub i, comparable to photon number densities eta sub tau, are assumed (where eta sub tau is approx. 3 times 10(exp 9) eta sub b). Furthermore, the required lepton number densities (L sub i eta sub tau) must be different for upsilon sub e than for upsilon sub mu and epsilon sub tau. It is shown that this loophole in the standard model of nucleosynthesis is robust and will not vanish as abundance and reaction rate determinations improve. However, it is also argued that theoretically (L sub e) approx. (L sub mu) approx. (L sub tau) approx. eta sub b is much less than eta sub tau which would preclude this loophole in standard unified models

Big-bang nucleosynthesis revisited

The homogeneous big-bang nucleosynthesis yields of D, He-3, He-4, and Li-7 are computed taking into account recent measurements of the neutron mean-life as well as updates of several nuclear reaction rates which primarily affect the production of Li-7. The extraction of primordial abundances from observation and the likelihood that the primordial mass fraction of He-4, Y(sub p) is less than or equal to 0.24 are discussed. Using the primordial abundances of D + He-3 and Li-7 we limit the baryon-to-photon ratio (eta in units of 10 exp -10) 2.6 less than or equal to eta(sub 10) less than or equal to 4.3; which we use to argue that baryons contribute between 0.02 and 0.11 to the critical energy density of the universe. An upper limit to Y(sub p) of 0.24 constrains the number of light neutrinos to N(sub nu) less than or equal to 3.4, in excellent agreement with the LEP and SLC collider results. We turn this argument around to show that the collider limit of 3 neutrino species can be used to bound the primordial abundance of He-4: 0.235 less than or equal to Y(sub p) less than or equal to 0.245

Big Bang nucleosynthesis and the Quark-Hadron transition

An examination and brief review is made of the effects of quark-hadron transistion induced fluctuations on Big Bang nucleosynthesis. It is shown that cosmologically critical densities in baryons are difficult to reconcile with observation, but the traditional baryon density constraints from homogeneous calculations might be loosened by as much as 50 percent, to 0.3 of critical density, and the limit on the number of neutrino flavors remains about N(sub nu) is less than or approximately 4. To achieve baryon densities of greater than or approximately 0.3 of critical density would require initial density contrasts R is much greater the 10(exp 3), whereas the simplest models for the transition seem to restrict R to less than of approximately 10(exp 2)