Exotic smooth structures and symplectic forms on closed manifolds

In this paper we discuss relations between symplectic forms and smooth structures on closed manifolds. Our main motivation is the problem if there exist symplectic structures on exotic tori. This is a symplectic generalization of a problem posed by Benson and Gordon. We give a short proof of the (known) positive answer to the original question of Benson and Gordon that there are no Kähler structures on exotic tori. We survey also other related results which give an evidence for the conjecture that there are no symplectic structures on exotic tori.     

From solar proton burning to pionic deuterium through the Nambu-Jona-Lasinio model of light nuclei

Within the Nuclear Nambu-Jona-Lasinio model of light nuclei (the NNJL model), describing strong low-energy nuclear interactions, we compute the width of the energy level of the ground state of pionic deuterium. The theoretical value fits well the experimental data. Using the cross-sections for the reactions _e + d p + p + e^- and _e + d p + n + _e, computed in the NNJL model, and the experimental values of the events of these reactions, detected by the SNO Collaboration, we compute the boron neutrino fluxes. The theoretical values agree well with the experimental data and the theoretical predictions within the Standard Solar Model by Bahcall. We argue the applicability of the constraints on the astrophysical factor for the solar proton burning, imposed by helioseismology, to the width of the energy level of the ground state of pionic deuterium. We show that the experimental data on the width satisfy these constraints. This testifies an indirect measurement of the recommended value of the astrophysical factor for the solar proton burning in terrestrial laboratories in terms of the width of the energy level of the ground state of pionic deuterium.     

Energy conditions,traversable wormholes and dust shells

Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the “volume integral quantifier,” which provides a measure of the “total amount” of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.     

Effect of parent and daughter deformation on half-life time in exotic decay

Taking Coulomb and proximity potential as interacting barrier for post-scission region we calculated half-life time for different modes of exotic decay treating parent and fragments as spheres and these values are compared with experimental data. We studied the effect of deformation of parent and daughter on half-life time treating emitted cluster as spherical. When deformations are included half-life time values are found to decrease, though slightly. It is found that parent deformation alone will not produce appreciable change in half-life time since it affects relatively small pre-scission part of the barrier.     

Collisional quenching of metastable states of antiprotonic helium by hydrogen and deuterium molecules

The quenching of metastable states of antiprotonic helium by collisions with hydrogen and deuterium molecules was studied. A systematic investigation of the delayed annihilation time spectra at various H₂ and D₂ admixture ratios at the ppm level revealed characteristic changes of their shape, which indicated a strong principal and orbital quantum number dependent quenching of levels in both cases. Applying a laser spectroscopy technique to measure the lifetimes of individual states and cascades we deduced H₂ and D₂ quenching cross-sections for the states (n, l )= (39, 35) and (37, 34). These cross-sections establish for D₂ molecules the strong increase of the quenching efficiency with increasing principal quantum number n of the state under investigation previously reported for the case of H₂ admixtures. Our experiments indicate that the low-n state (37, 34) is somewhat less affected by D₂ than by H₂, while the high-n state (39, 35) is equally quenched by both isotopes. Received 2 October 2000     

Resonant transmission of acoustic waves through an elastic plate quasiperiodically corrugated on surfaces

In this work, we study the resonant transmission of acoustic waves through a plate with quasiperiodic surface corrugations. The transmission spectrum shows peculiar transmission peaks, which cannot be simply attributed to the coherent diffraction as recognized previously in structured hard plates (without sustaining internal modes), whereas come from the resonant excitation of the coupled Stoneley surface modes in the elastic plate. The excitation frequencies can be determined by the geometrical structure factor of the quasiperiodic lattice, combining with the dispersion relation of the surface modes.     

Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions

In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ? × ? ^d with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [17 Kenig , C.E. , Merle , F. ( 2008 ). Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation . Acta Math. 201 : 147 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [26 Planchon , F. ( 2003 ). On uniqueness for semilinear wave equations . Math. Z. 244 : 587 – 599 .[Web of Science ®] , [Google Scholar]].     

Lattice Boltzmann methods for solving partial differential equations of exotic option pricing

This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.     

Positronium hydride formation in collisions of positrons with molecular hydrogen

Summary The feasibility of observing the threshold for the formation of positronium hydride, PsH, in collisions of low-energy positrons with hydrogen molecules in a mass spectrometric application is considered. The expected count rate of the signature ion H⁺ using existing positron beams depends upon the cross section for a dissociative attachment reaction. The estimation of this cross section relies on knowledge of certain potential energy curves and leptonic wave functions. This knowledge does not yet exist. The curves are roughly estimated by considering the binding of a positron to the ionicB state of H₂. Methods of calculating the wave functions are briefly considered.A preliminary version was presented at the Third International Workshop on Positron and Positronium Chemistry, Milwaukee, July 1990 (Ref. [1])     

超高层建筑受大型高速飞行物撞击所致非连续性坍塌模拟与研究

为了解大型高速飞行物撞击超高层建筑后,建筑物塌落过程及其特征,使用基于颗粒流的PFC3D作为平台对坍塌过程进行模拟。所构建的超高层建筑为核心筒-框架结构,飞行物由较大的三个颗粒组成,其撞击速度为720km/h,撞击高度为建筑侧面250m和100m。研究了撞击物进入层间运动的特征,及在两种高度撞击后的坍塌过程。模拟结果表明,飞行物非直接撞击核心筒时建筑不会发生整体破坏,核心筒的受撞破坏是建筑坍塌破坏的关键。建筑高处受撞击后坍塌可分为两个阶段,其现象和原因各不相同。指出了建筑高处和低处受撞坍塌过程的三点不同。最后分析了撞击塌落后的地面影响范围及特征。