Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

Multiscale Analysis in Momentum Space for Quasi-periodic Potential in Dimension Two

We consider a polyharmonic operator H=(-\Delta)^l+V(\x) in dimension two with $l\geq 2$, $l$ being an integer, and a quasi-periodic potential V(\x). We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i}$ at the high energy region. Second, the isoenergetic curves in the space of momenta \k corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results.Comment: 125 pages, 4 figures. arXiv admin note: incorporates arXiv:1205.118

Limb diversity and digit reduction in reptilian evolution

Journal ArticleThe study of morphological rules, or trends, offered classical biologists the opportunity to address the mechanisms underlying the evolution of anatomical designs. Regularities in evolution suggested that common functional or developmental rules governed the transformation of structures. Parallelism is one such example

MODELLING THE ELECTRON WITH COSSERAT ELASTICITY

Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the body–fluid interaction holding for the case of many bodies

Study on Modification of Lignin as Dispersant of Aqueous Graphene Suspension and Corrosion Performance in Waterborne G/Epoxy Coating

Though graphene (G) as an excellent protective material for metal, it can aggravate metal corrosion in other side. The modification of sodium lignin sulfonate was achieved by using itaconic acid and acrylamide，which was proved by UV-vis and Raman spectra. The modified sodium lignin sulfonate (LAI) with more carboxylic groups can be used as the dispersant for aqueous graphene suspension. The commercial graphene can be dispersed uniformly and stability in water via π-π interaction with LAI at high concentration (6 mg/mL)，and the LAI-G system can be used as an inhibitor in waterborne epoxy coatings too. Electrochemical impedance spectroscope (EIS) and Tafel polarization curves showed that the corrosion performance of waterborne epoxy system with well-dispersed G (0.5 wt %) was remarkably improved compared with pure epoxy coating

The feeding system of <i>Tiktaalik roseae</i>: an intermediate between suction feeding and biting

Changes to feeding structures are a fundamental component of the vertebrate transition from water to land. Classically, this event has been characterized as a shift from an aquatic, suction-based mode of prey capture involving cranial kinesis to a biting-based feeding system utilizing a rigid skull capable of capturing prey on land. Here we show that a key intermediate, Tiktaalik roseae, was capable of cranial kinesis despite significant restructuring of the skull to facilitate biting and snapping. Lateral sliding joints between the cheek and dermal skull roof, as well as independent mobility between the hyomandibula and palatoquadrate, enable the suspensorium of T. roseae to expand laterally in a manner similar to modern alligator gars and polypterids. This movement can expand the spiracular and opercular cavities during feeding and respiration, which would direct fluid through the feeding apparatus. Detailed analysis of the sutural morphology of T. roseae suggests that the ability to laterally expand the cheek and palate was maintained during the fish-to-tetrapod transition, implying that limited cranial kinesis was plesiomorphic to the earliest limbed vertebrates. Furthermore, recent kinematic studies of feeding in gars demonstrate that prey capture with lateral snapping can synergistically combine both biting and suction, rather than trading off one for the other. A “gar-like” stage in early tetrapod evolution might have been an important intermediate step in the evolution of terrestrial feeding systems by maintaining suction-generation capabilities while simultaneously elaborating a mechanism for biting-based prey capture

Extended States for Polyharmonic Operators with Quasi-periodic Potentials in Dimension Two

We consider a polyharmonic operator H=(-\Delta)^l+V(\x) in dimension two with $l\geq 2$, $l$ being an integer, and a quasi-periodic potential V(\x). We prove that the spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^{i}$ at the high energy region. Second, the isoenergetic curves in the space of momenta \k corresponding to these eigenfunctions have a form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results.Comment: This is an announcement only. Text with the detailed proof is under preparation. 11 pages, 4 figures. arXiv admin note: text overlap with arXiv:math-ph/0601008, arXiv:0711.4404, arXiv:1008.463

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.Comment: 41 pages, 7 figure

Ossification patterns of the carpus and tarsus in salamanders and impacts of preaxial dominance on the fin-to-limb transition

Early limb skeletogenesis in salamanders is characterized by preaxial elements, digits I and II forming earlier than their postaxial counterparts (digits III to V), a phenomenon known as preaxial dominance, whereas in amniotes and anurans, these developmental sequences are reversed. This pattern characterizes the late skeletogenesis of digits and zeugopodium of anamniote tetrapods but remains unknown in carpals/tarsals. To correct this gap in knowledge, we investigate the ossification patterns of the carpals/tarsals in six salamander families/clades based on micro–computed tomography scans. We found that preaxial dominance is seen in the distal carpals/tarsals of several salamander clades and diverse early tetrapods, such as temnospondyls and amniotes. This distribution suggests that preaxial dominance is a primitive developmental pattern in tetrapods. Our results demonstrate that the distal carpals/tarsals are developmentally and evolutionarily independent in the autopodium, and preaxial dominance facilitates stabilization of the number of distal carpals/tarsals during fin-to-limb transition and digit reduction in early tetrapods