Symmetries in a very special relativity and isometric group of Finsler space

We present an explicit connection between the symmetries in a Very Special Relativity (VSR) and isometric group of a specific Finsler space. It is shown that the line element that is invariant under the VSR symmetric group is a Finslerian one. The Killing vectors in Finsler space are constructed in a systematic way. The Lie algebras corresponding to the symmetries of VSR are obtained from a geometric famework. The dispersion relation and the Lorentz invariance violation effect in the VSR are discussed.     

Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system

The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation.     

Symmetry groups and spiral wave solution of a wave propagation equation

We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.     

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.     

Lie symmetries and invariants of constrained Hamiltonian systems

According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.     

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.     

Chemical composition of the lunar surface from neutron leakage fluxes

The neutron leakage fluxes from the lunar surface are calculated by Monte Carlo transport code based on Geant4. The integral fluxes of fast neutrons, epi-thermal neutrons and thermal neutrons are analyzed. Numerical results for 20 kinds of lunar soils and 7 minerals show that the fast neutron fluxes are linearly related to the average atomic mass numbers of the lunar materials used in simulations. Meanwhile, the average atomic mass numbers are strongly modulated by the abundances of iron (Fe) and titanium (Ti), and a linear relationship between the average atomic mass numbers and the abundances of Fe and Ti is found. Furthermore, the results show that the ratios of epi-thermal to thermal fluxes for lunar soils are linearly related to the macroscopic absorption cross sections of lunar materials, and that the macroscopic absorption cross sections monotonically increase with the abundances of Fe and Ti by a simple function. Then we reach the conclusion that the neutron fluxes can provide the information about the Fe and Ti contents.     

Study of the Lie symmetries of a relativistic variable mass system

The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result.     

Modification of Boundary Fluctuations by LHCD in the HT—7 Tokamak

Measurements of boundary fluctuations and fluctuation driven electron fluxes have been performed in ohmic and lower hybrid current drive enhanced confinement plasma using a graphite Langmuir probe array on HT-7 tokamak. The fluctuations are significantly suppressed and the turbulent fluxes are remarkably depressed in the enhanced plasma. We characterized the statistical properties of fluctuations and the particle flux and found a non-Gaussian character in the whole scrape-off layer with minimum deviations from Gaussian in the proximity of the velocity shear layer in ohmic plasma. In the enhanced plasma the deviations in the boundary region are all reduces obviously. The fluctuations and induced electron fluxes show sporadic bursts asymmetric in time and the asymmetry is remarkably weakened in the lower hybrid current driving (LHCD) phase. The results suggest a coupling between the statistical behaviour of fluctuations and the turbulent flow.     

Perturbation of Symmetries and Mei Adiabatic Invariants of Nonholonomic Systems with Servoconstraints

The perturbation of symmetries and Mei adiabatic invariants of nonholonomic systems with servoconstraints are studied. The exact invariants in the form of Mei conserved quantities introduced by the Mei symmetry of nonholonomic systems with servoconstraints without perturbations are given. Based on the definition of higher-order adiabatic invariants of mechanical systems, the perturbation of Mei symmetries for nonholonomic .systems with servoconstraints under the action of small disturbance is investigated, and Mei adiabatic invatiants of the system are obtained. An example is given to illustrate the application of the results.     

Observation of "Stick" and "Handle" intermediates along the fullerene road

The hypothesis that fullerenes grow in a carbon plasma by the addition of C2 units (the "fullerene road") has been widely acclaimed as the most plausible mechanism for formation of larger fullerenes including C60 and C70. Calculations suggest that the association of C2 with fullerenes proceeds through two classes of intermediates, "sticks" and "handles." Here we report the observation of these species using high-resolution ion-mobility measurements for C(n) cations generated by laser vaporization of graphite and laser desorption of C60. Sticks with up to eight-atom chains have also been found.     

最具潜力的新型"奇迹材料"——石墨烯

2009年4月29日据物理世界网报道,意大利的科研人员成功地用石墨烯制造了首枚包含两个晶体管的集成电路(见封面主图),它拥有简单的计算能力,标制着碳基电子学时代的到来.这枚只有两个晶体管的集成电路虽然很小,却是向制造碳基高性能电子器件迈出的重要一步.     

Ccontrolling the Transition Between "Higher" and "Lower" State of OB in Coherent Atomic Medium

We present a new experimental demonstration that the threshold points and shape of OB hysteresis curve in a four-level Rb atomic system inside an optical cavity were controllably changed by optical signals.Tuning the triggering optical signal to two different transitions of the atomic system we found that the OB threshold points shift toward different direction and at the same time the shape of the OB curve is also changed.For a given intensity of probe laser the OB system can be reliably inversed from its lower stable state to upper state under the triggering of a suitably tuned optical pulse signal (we named it up-controlling signal).More interesting, the inversed OB state does not drop to its initial lower stable state after the triggering pulse signal has passed, but moves to the upper branch of the initial OB curve and stably stays there until another optical signal tuned on other atomic transition (named down-controlling signal) coming.The result shows that there is the ability of information storage in the OB system.The experiments are reasonably explained with the change of cavity resonant condition resulting from the enhanced third-order nonlinearity in multilevel atomic system owing to atomic coherence.     

Comment on "Pushing the hyperpolarizability to the limit"

It is shown that energy/length scaling complicates maximizing the first hyperpolarizability of a single electron as a function of the potential. A more transparent formula for this hyperpolarizability is given. Examining this formula demonstrates that Zhou et al.(1) have not proved that modulated conjugation results in large hyperpolarizability.     

Viewing the proton through "color" filters

While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type quark and gluon distributions which depict a full-3D proton at every fixed light-cone momentum, like what is seen through momentum ("color") filters. After appropriate phase-space reductions, the Wigner distributions are related to the generalized parton distributions (GPDs) and transverse-momentum dependent parton distributions, which are measurable in high-energy experiments. The new interpretation of GPDs provides a classical way to visualize the orbital motion of the quarks, which is known to be the key to the spin and magnetic moment of the proton.     

Unraveling the "pressure effect" in nucleation

The influence of the pressure of a chemically inert carrier gas on the nucleation rate is one of the biggest puzzles in the research of gas-liquid nucleation. Experiments can show a positive effect, a negative effect, or no effect at all. The same experiment may show both trends for the same substance depending on temperature, or for different substances at the same temperature. We show how this ambiguous effect naturally arises from the competition of two contributions: nonisothermal effects and pressure-volume work. Our model clarifies seemingly contradictory experimental results and quantifies the variation of the nucleation ability of a substance in the presence of an ambient gas. Our findings are corroborated by molecular dynamics simulations and might have important implications since nucleation in experiments, technical applications, and nature practically always occurs in the presence of an ambient gas.