Embedding of non-simple Lie groups,coupling constant relations and non-uniqueness of models of unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU _L (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU _L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU _L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin²ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE ₆, while addition of extra charged fermion singlets can reduce the value of sin² ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.     

From Rényi Entropy Power to Information Scan of Quantum States

In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.     

炸药爆炸驱动下铜板的层裂现

在进行炸药驱动铜板实验中,用激光速度干涉仪(VISAR)记录铜板自由面速度,观察到了铜板层裂现象,并用非线性有限元方法对爆炸载荷下铜板层裂过程进行数值模拟分析,得到了与实验结果吻合的计算结果。     

Topological recursion relations from Pixton relations

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.     

Fucoidan‐Mimetic Glycopolymers as Tools for Studying Molecular and Cellular Responses in Human Blood Platelets

The marine sulfated polysaccharide fucoidan displays superior ability to induce platelet aggregation compared to other sulfated polysaccharides. As such, it is an attractive tool for studying molecular and cellular responses in activated platelets. The heterogeneous structure, however, poses a problem in such applications. This study describes the synthesis of sulfated α‐l ‐fucoside‐pendant poly(methacryl amides) with homogeneous structures. By using both thiol‐mediated chain transfer and reversible addition‐fragmentation chain transfer polymerization techniques, glycopolymers with different chain lengths are obtained. These glycopolymers show platelet aggregation response and surface changes similar to those of fucoidan, and cause platelet activation through intracellular signaling as shown by extensive protein tyrosine phosphorylation. As the platelet activating properties of the glycopolymers strongly mimic those of fucoidan, this study concludes these fucoidan‐mimetic glycopolymers are unique tools for studying molecular and cellular responses in human blood platelets.

     

Shock jump relations for multiphase mixtures with stiff mechanical relaxation

Examples of multiphase mixtures for which velocity and pressure relaxation are a stiff phenomenon are involved in many practical applications dealing with condensed phase mixtures, solid alloys, propellants and solid explosives, specific composite materials, micro- and nano-structured mixtures, etc. Shock relations for the mixture necessitate the determination of the volume fraction jump or any other thermodynamic variable jump. Examination of the shock dispersion mechanism suggests such jump relations. These relations are the phase Hugoniots which are compatible with the mixture energy equation. The corresponding model is conservative and symmetric. It fulfils the single-phase limit and guarantees volume fraction positivity. The shock relations are validated over a large set of experimental data and provide a remarkable agreement. R. Saurel, O. Le Métayer, J. Massoni and S. Gavrilyuk also belong to INRIA SMASH Project.     

Anisotropic damage mechanics for viscoelastic ice

We present a formulation of continuum damage in glacier ice that incorporates the induced anisotropy of the damage effects but restricts these formally to orthotropy. Damage is modeled by a symmetric second rank tensor that structurally plays the role of an internal variable. It may be interpreted as a texture measure that quantifies the effective specific areas over which internal stresses can be transmitted. The evolution equation for the damage tensor is motivated in the reference configuration and pushed forward to the present configuration. A spatially objective constitutive form of the evolution equation for the damage tensor is obtained. The rheology of the damaged ice presumes no volume conservation. Its constitutive relations are derived from the free enthalpy and a dissipation potential, and extends the classical isotropic power law by elastic and damage tensor dependent terms. All constitutive relations are in conformity with the second law of thermodynamics.PACS 83.60.Df, 62.20.Mk