Shilnikov Lemma for a nondegenerate critical manifold of a Hamiltonian system

We prove an analog of Shilnikov Lemma for a normally hyperbolic symplectic critical manifold $M\subset H^{-1}(0)$ of a Hamiltonian system. Using this result, trajectories with small energy $H=\mu>0$ shadowing chains of homoclinic orbits to $M$ are represented as extremals of a discrete variational problem, and their existence is proved. This paper is motivated by applications to the Poincar\'e second species solutions of the 3 body problem with 2 masses small of order $\mu$. As $\mu\to 0$, double collisions of small bodies correspond to a symplectic critical manifold of the regularized Hamiltonian system

Observation of the Fractional Quantum Hall Effect in Graphene

When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields

The first basic boundary value problem of Riemann's type for bianalytical functions in a plane with slots

The paper is devoted to the investigation of one of the basic boundary value problems of Riemann's type for bianalytical functions. In the course of work there was made out a constructive method for solution of the problem given in a plane with slots. There was also found out that the solution of the problem under consideration consists of consequent solutions of two Riemann's boundary value problems for analytical functions in a plane with slots. Besides, a picture of solvability of the problem is being searched and its Noether is identified. Apie pirmojo pagrindinio kraštinio Rimano tipo uždavinio bianalizinėms funkcijoms plokštumoje su įtrūkiai sprendimą Santrauka Šiame darbe tyrinejamas uždavinys, kai ieškoma dalimis bianaliziniu funkciju, nykstančiu begalybeje, apribotu greta kontūro trūkio tašku ir šiame kontūre tenkinančiu dvi kraštines salygas. Parodoma, kad sprendžiamas uždavinys suvedamas i sprendima dvieju Rimano uždaviniu analizinems funkcijoms. First Published Online: 14 Oct 201

Efficiency of monolaurin in mitigating ruminal methanogenesis and modifying C-isotope fractionation when incubating diets composed of either C3 or C4 plants in a rumen simulation technique (Rusitec) system

Mitigation of methanogenesis in ruminants has been an important goal for several decades. Free lauric acid, known to suppress ruminal methanogenesis, has a low palatability; therefore, in the present study the aim was to evaluate the mitigation efficacy of its esterified form (monolaurin). Further, 13C-isotope abundance (δ13C) and 13C-12C fractionation during methanogenesis and fermentation were determined to evaluate possible microbial C-isotope preferences. Using the rumen simulation technique, four basal diets, characterised either by the C3 plants grass (hay) and wheat (straw and grain), or the C4 plant (13C excess compared with C3 plants) maize (straw and grain), and a mixture of the latter two, were incubated with and without monolaurin (50g/kg dietary DM). Added to hay, monolaurin did not significantly affect methanogenesis. When added to the other diets (P<0·05 for the wheat-based diet) methane formation was lowered. Monolaurin decreased fibre disappearance (least effect with the hay diet), acetate:propionate ratio, and protozoal counts. Feed residues and SCFA showed the same δ13C as the diets. Methane was depleted in 13C while CO2 was enriched in 13C compared with the diets. Monolaurin addition resulted in 13C depletion of CO2 and enrichment in CH4 (the latter only in the hay diet). In conclusion, monolaurin proved to effectively decrease methanogenesis in the straw-grain diets although this effect might partly be explained by the concomitantly reduced fibre disappearance. The influence on 13C-isotope abundance and fractionation supports the hypothesis that ruminal microbes seem to differentiate to some extent between C-isotopes during methanogenesis and fermentatio

Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene

Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly susceptible to electronic interactions, and expected to undergo a phase transition into a state with spontaneous broken symmetries. By systematically investigating a large number of singly- and doubly-gated bilayer graphene (BLG) devices, we show that an insulating state appears only in devices with high mobility and low extrinsic doping. This insulating state has an associated transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly suggesting a gapped broken symmetry state that is destroyed by very weak disorder. The transition to the intrinsic broken symmetry state can be tuned by disorder, out-of-plane electric field, or carrier density

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Role of peripheral quantitative computed tomography in identifying disuse osteoporosis in paraplegia

Objective: Disuse osteoporosis is a major long-term health consequence of spinal cord injury (SCI) that still needs to be addressed. Its management in SCI should begin with accurate diagnosis, followed by targeted treatments in the most vulnerable subgroups. We present data quantifying disuse osteoporosis in a cross-section of the Scottish paraplegic population to identify subgroups with lowest bone mineral density (BMD). Materials and Methods: Forty-seven people with chronic SCI at levels T2-L2 were scanned using peripheral Quantitative Computed Tomography (pQCT) at four tibial sites and two femoral sites, at the Queen Elizabeth National Spinal Injuries Unit, Glasgow (U.K.). At the distal epiphyses, trabecular BMD (BMDtrab), total BMD, total bone cross-sectional area (CSA), and bone mineral content (BMC) were determined. In the diaphyses, cortical BMD, total bone CSA, cortical CSA, and BMC were calculated. Bone, muscle and fat CSAs were estimated in the lower leg and thigh. Results: BMDtrab decreased exponentially with time since injury, at different rates in the tibia and femur. At most sites, female paraplegics had significantly lower BMC, total bone CSA and muscle CSA than male paraplegics. Subjects with lumbar SCI tended to have lower bone values and smaller muscle CSAs than in thoracic SCI. Conclusion: At the distal epiphyses of the tibia and femur, there is generally a rapid and extensive reduction in BMDtrab after SCI. Female subjects, and those with lumbar SCI, tend to have lower bone values than males or those with thoracic SCI, respectively. Keywords: Bone loss, osteoporosis, paraplegia, peripheral Quantitative Computed Tomography, spinal cord injur

Screening and interlayer coupling in multilayer graphene field-effect transistors

With the motivation of improving the performance and reliability of aggressively scaled nano-patterned graphene field-effect transistors, we present the first systematic experimental study on charge and current distribution in multilayer graphene field-effect transistors. We find a very particular thickness dependence for Ion, Ioff, and the Ion/Ioff ratio, and propose a resistor network model including screening and interlayer coupling to explain the experimental findings. In particular, our model does not invoke modification of the linear energy-band structure of graphene for the multilayer case. Noise reduction in nano-scale few-layer graphene transistors is experimentally demonstrated and can be understood within this model as well.Comment: 13 pages, 4 figures, 20 reference

Performance of Monolayer Graphene Nanomechanical Resonators with Electrical Readout

The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical (NEMS) applications. We demonstrate fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the MHz range. The strong dependence of the resonant frequency on applied gate voltage can be fit to a membrane model, which yields the mass density and built-in strain. Upon removal and addition of mass, we observe changes in both the density and the strain, indicating that adsorbates impart tension to the graphene. Upon cooling, the frequency increases; the shift rate can be used to measure the unusual negative thermal expansion coefficient of graphene. The quality factor increases with decreasing temperature, reaching ~10,000 at 5 K. By establishing many of the basic attributes of monolayer graphene resonators, these studies lay the groundwork for applications, including high-sensitivity mass detectors