Differentiable circle maps with a flat interval

We study weakly order preserving circle maps with a flat interval, which are differentiable even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from degenerate geometry to bounded geometry, depending on the degree of the singularities at the boundary of the flat interval.Partially supported by KBN grant Iteracje i Fraktale #210909101.     

Differentiable structure for direct limit groups

A direct limit of (finite-dimensional) Lie groups has Lie algebra and exponential map exp _G : gG. BothG and g carry natural topologies.G is a topological group, and g is a topological Lie algebra with a natural structure of real analytic manifold. In this Letter, we show how a special growth condition, natural in certain physical settings and satisfied by the usual direct limits of classical groups, ensures thatG carries an analytic group structure such that exp _G is a diffeomorphism from a certain open neighborhood of 0g onto an open neighborhood of 1 _G G. In the course of the argument, one sees that the structure sheaf for this analytic group structure coincides with the direct limit C (G ) of the sheaves of germs of analytic functions on theG .L.N. partially supported by a University of California Dissertation Year Fellowship.E.R.C. partially supported by N.S.F. Grant DMS 89 09432.J.A.W. partially supported by N.S.F. Grant DMS 88 05816.     

An Asymptotic Comparison of Differentiable Dynamics and Tropical Geometry

In this paper we introduce a new comparison method to give rough asymptotic estimates of different evolutional dynamics. It uses a kind of scale transform called tropical geometry, which connects automata with real rational dynamics. By this procedure the defining equations are transformed rather than solutions themselves. Real rational dynamics is regarded as an approximation of evolutional dynamics given by partial differential equations (PDEs). Two different evolutional dynamics can be considered when their defining equations are transformed to the same automata at infinity.     

Differentiable programming and density matrix based Hartree–Fock method

Differentiable programming is an emerging programming paradigm that allows people to take derivative of an output of arbitrary code snippet with respect to its input. It is the workhorse behind several well known deep learning frameworks,and has attracted significant attention in scientific machine learning community. In this paper, we introduce and implement a density matrix based Hartree–Fock method that naturally fits into the demands of this paradigm, and demonstrate it by performing fully variational ground state calculation on several representative chemical molecules.     

Natural-Convection Thermosyphon Heat Transfer from a Stack of Horizontal Plates

Steady laminar natural convection of water about vertically stacked, two-sided, horizontal heated plates was studied experimentally over a range of plate gap to plate half-width ratio, H/a, from 0.078 to 0.94. Measurements were made of power input per plate, plate temperatures, and inlet and outlet bulk fluid temperatures. From these data were determined average Nusselt and Rayleigh numbers for each plate, which were correlated with a power law Nu = C Raⁿ for each gap height. The Nusselt numbers increased with gap height up to H/a 0.47 (from 8 to 48), and then became independent of H/a. The exponent n increased from n 0.2 at the lowest gap height tested (H/a 0.078), to a high value of n approximately equal to 0.4 at H/a = 0.24 and then decreased back to n = 0.2 for H/a greater than or equal to 0.47.     

The Virtual Class of the Moduli Stack of Stable r-Spin Curves

We recall the outline of the Seely-Singer-Witten construction of the virtual class on the moduli of stable r-spin curves. We prove that the obtained classes satisfy the axioms of Jarvis-Kimura-Vaintrob.     

Effective Stability for Gevrey and Finitely Differentiable Prevalent Hamiltonians

For perturbations of integrable Hamiltonian systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is analytic. This fundamental result has been extended in two distinct directions. The first one is due to Niederman, who showed that under the analyticity assumption, the result holds true for a prevalent class of integrable systems which is much wider than the steep systems. The second one is due to Marco-Sauzin but it is limited to quasi-convex integrable systems, for which they showed exponential stability if the system is assumed to be only Gevrey regular. If the system is finitely differentiable, we showed polynomial stability, still in the quasi-convex case. The goal of this work is to generalize all these results in a unified way, by proving exponential or polynomial stability for Gevrey or finitely differentiable perturbations of prevalent integrable Hamiltonian systems.     

A model of Photoinduced Regular-Dimerized Stack Transitions

We present a model of photoinduced regular-dimerized stack transitions and discuss theoretically the behavior of the organic molecular mixed-stack charge-transfer crystal, Tetrathiafulvalene-Chloranil (TTF-CA). We investigate both the photoinduced structural phase transitions and the thermal phase transition between the regular-stack neutral phase at high temperatures and the dimerized-stack ionic phase at low temperatures. Our model is based on a simple phenomenological insight that the molecules have three stable displacements in the crystal. The cooperative effect is accounted for by introducing harmonic coupling between the molecules. It is the first attempt to include not only the photo-excitation but also the temperature effect on an equal footing.     

量子限制斯达克效应对三角形量子阱吸光特性的影响

本文通过计算量子力学波动方程以及载流子传输特性,哈密顿量的H能谱图和边界条件等的理论方法来分析量子限制斯达克效应对三角形量子阱体系吸收特性的影响,说明了选择合适的量子阱垒层对于提高三角形量子阱吸光率具有重要的意义。     

基于可逆固体氧化物电池堆的电能高效存储

研究了固体氧化物电池堆中电能的可逆存储与产生,通过相变金属存储燃料电池模式下的热能并在电解池模式下加以利用. 系统的荷电状态(即氢燃料百分比)可显著增加开路电压,系统压力的增加有效提高了开路电压. 较高的系统压力可促进电极表面的物质扩散和输运,相应地改善电极的极化电阻. 通过有效的热能管理,系统的电能可逆存储的循环效率可高达92%.     

角度调谐滤光片特性分析及膜系设计

对窄带滤光片的倾斜入射特性作了分析.斜入射时其透射通带和峰值会向短波方向移动,透射曲线的稳定性跟滤光片的间隔层结构相关,多腔间使用相同的间隔层可以保证斜入射时有稳定的峰值透射率和带宽,利用该特点可以制备角度调谐窄带滤光片.透射光S和P偏振分量的中心波长随入射角度的增大出现分离现象,产生较大的偏振相关损耗.通过搭配不同厚度的高低折射率材料作为间隔层,改变其有效折射率,使其两个偏振分量的中心波长实现重合.设计了符合密集波分复用(Dense Wavelength Division Multiplexing,DWDM)系统要求的低偏振相关损耗四腔窄带角度调谐滤光片膜系,其可调谐范围达20 nm以上,并评估了所设计角度调谐滤光片的调谐性能.     

Three Dimensional Monitoring of Stack Plume Dynamics by a Scanning Mie Lidar System as a Plume Watchdog Station

A scanning lidar system was developed to watch the nighttime diffusion process of plume from a smokestack of a large incinerator located around 3 km from the system. Observed data sets were visualized as three dimensional images in which could be seen the diffusion pattern from any direction, and this made it easy to investigate the exhaust dynamics. Observation results showed that the original plume extended at least 1.6 km, where there was a residential area, from the smokestack increasing in diameter to about 500 m. High density aerosols originating from the smokestack were measured in that area even at midnight. The lidar system performance as a plume watchdog station was discussed from the standpoint of publichealth-related plume monitoring.     

抗水性光致聚合物的体全息存储研究

提出了基于酞菁染料的全息记录材料,与目前已报道的基于丙烯酞胺基单体光聚合型全息记录介质相比,该聚合体系显示了优良的全息特性：全“干”热后处理,良好的抗水性和环境稳定性,制备过程简单和低毒性,并可制备成较厚的感光膜层。针对存储过程的页间和页内串扰做了理论分析和MTALAB仿真,采用自主研制的抗水性光致聚合物材料记录多幅不同图像的实验方案,分析了本抗水性全息材料的角度复用性能。     

The Volume of the Moduli Space of Flat Connections on a Nonorientable 2-Manifold

We compute the Riemannian volume of the moduli space of flat connections on a nonorientable 2-manifold, for a natural class of metrics. We also show that Wittens volume formula for these moduli spaces may be derived using Haar measure, and we give a new proof of Wittens volume formula for the moduli space of flat connections on a 2-manifold using Haar measure.     

Three-Body Physics in a Finite Volume

Three particles with large two-body scattering lengths display universal properties including a spectrum of three-body bound states called “Efimov trimers”. I calculate the spectrum of three identical bosons inside a finite cubic box below the three-body breakup threshold. The dependence of the spectrum on the box size and the effects of the breakdown of spherical symmetry are investigated using effective field theory. The renormalization of the effective field theory in the finite volume is explicitly verified. The study of the three-nucleon system inside a finite cubic volume provides a tool for the understanding of Lattice QCD results. I study the triton in a finite volume at physical and unphysical pion masses.     

危化品仓库堆垛安全距离的精确扫描定位监控算法的研究

根据危化品仓库码垛安全距离需要精确监控的需求,设计开发了一种精确扫描定位装置,将仓库划分为若干网格,对每个监测面测距扫描,获得每一个点的距离值和角度值,根据对应点是否与安全状态数值一致来判断堆垛的安全状态。硬件由控制器、细分驱动、步进电机、涡轮螺杆、工作台等组成。电机定位控制采用指数型加减速算法和闭环反馈调节相结合的控制算法,首先获得一个起跳频率,经过加减速控制阶段,到达目标位置附近,之后进入反馈调节阶段,控制步进电机到达指定位置。指数型加减速算法降低了启动和停止时加速度突变大小,避免了由于步进电机频率变化过快引起失步和堵转。实验结果表明,该装置及算法运行稳定,定位精度在 0.022度左右,定位精度高,满足仓库安全距离扫描监控的精度要求。     

Volume reflection of a proton beam in a bent crystal

Volume reflection predicted in the mid-1980s by Taratin and Vorobiev has been observed for the first time in the interactions of a 70 GeV proton beam with a short bent crystal. Incident protons deviate from convex atomic planes in the bulk of the crystal as a result of coherent interaction with bent lattice around the tangency point of particle trajectory with a curved atomic plane. The deflection angle 2theta(R) was found to be (39.5+/-2.0) microrad, or (1.65+/-0.08)theta(c) in terms of the critical angle for channeling. The process has a large probability with respect to channeling and takes place in the angular range equal to the bend angle of atomic planes. It could possibly open new fields of application of crystals in high-energy particle beam optics.     

The Infinite Volume Limit of Dissipative Abelian Sandpiles

We construct the thermodynamic limit of the stationary measures of the Bak-Tang-Wiesenfeld sandpile model with a dissipative toppling matrix (sand grains may disappear at each toppling). We prove uniqueness and mixing properties of this measure and we obtain an infinite volume ergodic Markov process leaving it invariant. We show how to extend the Dhar formalism of the abelian group of toppling operators to infinite volume in order to obtain a compact abelian group with a unique Haar measure representing the uniform distribution over the recurrent configurations that create finite avalanchesWork partially supported by Tournesol project – nr. T2001.11/03016VF     

The Volume Element of Space-Time and Scale Invariance

Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form S= L ₁ d ⁴ x+ L ₂ d ⁴ x where the volume element d ⁴ x is independent of the metric. For global scale invariance, a dilaton has to be introduced, with non-trivial potentials V()=f ₁ e in L ₁ and U()=f ₂ e ² in L ₂ . This leads to non-trivial mass generation and a potential for which is interesting for inflation. Interpolating models for natural transition from inflation to a slowly accelerated universe at late times appear naturally. This is also achieved for Quintessential models, which are scale invariant but formulated with the use of volume element d ⁴ x alone. For closed strings and branes (including the supersymmetric cases), the modified measure formulation is possible and does not require the introduction of a particular scale (the string or brane tension) from the begining but rather these appear as integration constants.