Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System

We study a system of rods onℤ², with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N = 2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.     

Entropy-Driven Phase Transitions in Multitype Lattice Gas Models

In multitype lattice gas models with hard-core interaction of Widom–Rowlinson type, there is a competition between the entropy due to the large number of types, and the positional energy and geometry resulting from the exclusion rule and the activity of particles. We investigate this phenomenon in four different models on the square lattice: the multitype Widom–Rowlinson model with diamond-shaped resp. square-shaped exclusion between unlike particles, a Widom–Rowlinson model with additional molecular exclusion, and a continuous-spin Widom–Rowlinson model. In each case we show that this competition leads to a first-order phase transition at some critical value of the activity, but the number and character of phases depend on the geometry of the model. We also analyze the typical geometry of phases, combining percolation techniques with reflection positivity and chessboard estimates.     

Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.     

空气孔辅助光纤的模式截止

光纤的截止波长是光纤设计的重要参量之一。利用全矢量正交函数模型对空气孔辅助光纤的模式截止特性进行了讨论。分析表明：由于光纤包层中存在空气孔,即使不考虑材料色散,包层的有效折射率也与波长有关;包层有效折射率由包层中空气孔的大小和波长决定,与芯子的掺杂浓度无关。在所研究的波长范围之内,与传统的w型光纤类似,在包层中空气孔的相对尺寸d／Λ较大时出现了基模截止现象。d／Λ从0．2到0．9变化时,光纤的各阶模式的截止波长都随之减小;各阶模式的截止波长随d／Λ变化曲线的斜率随模式阶次的升高而降低。     

Experimental Validation of Entropy-Driven Swarm Exploration under Sparsity Constraints with Sparse Bayesian Learning

Increasing the autonomy of multi-agent systems or swarms for exploration missions requires tools for efficient information gathering. This work studies this problem from theoretical and experimental perspectives and evaluates an exploration system for multiple ground robots that cooperatively explore a stationary spatial process. For the distributed model, two conceptually different distribution paradigms are considered. The exploration is based on fusing distributively gathered information using Sparse Bayesian Learning (SBL), which permits representing the spatial process in a compressed manner and thus reduces the model complexity and communication load required for the exploration. An entropy-based exploration criterion is formulated to guide the agents. This criterion uses an estimation of a covariance matrix of the model parameters, which is then quantitatively characterized using a D-optimality criterion. The new sampling locations for the agents are then selected to minimize this criterion. To this end, a distributed optimization of the D-optimality criterion is derived. The proposed entropy-driven exploration is then presented from a system perspective and validated in laboratory experiments with two ground robots. The experiments show that SBL together with the distributed entropy-driven exploration is real-time capable and leads to a better performance with respect to time and accuracy compared with similar state-of-the-art algorithms.     

Cutoff behaviour of graded-index slab waveguides

The cutoff behaviour of graded-index planar waveguides is analysed in terms of the normalized waveguide parameters by using the multilayer technique and the WKB approach. The results show a very high degree of accuracy when checked against exact known values for exponential and hyperbolic index profiles. A set of universal plots showing the general features is given for the cutoff values of both fundamental and first-order modes. The TM polarization is also studied by comparison with the TE one.     

Cutoff dependence of the Casimir effect

The problem of calculating the Casimir force on two conducting planes by means of the stress tensor is examined. The evaluation of this quantity is carried out using an explicit regularization procedure which has its origin in the underlying (2+1) dimensional Poincaré invariance of the system. The force between the planes is found to depend on the ratio of two independent cutoff parameters, thereby rendering any prediction for the Casimir effect an explicit function of the particular calculational scheme employed. Similar results are shown to obtain in the case of the conducting sphere. Received: 15 October 2000 / Revised version: 10 January 2001 / Published online: 6 April 2001     

Cutoff solitons in axially uniform systems

The optical response of axially uniform nonlinear photonic bandgap fibers is studied theoretically. We observe gap-soliton-like generation and associated bistability, similar to what is typically found in periodically modulated nonlinear structures. This response stems from the nature of the guided-mode dispersion relations, which involve a frequency cutoff at zero wave vector. In such systems, solutions with zero group velocities and minimal coupling to radiation modes come in naturally. We term such solitons "cutoff solitons"; they provide an interesting alternative to gap solitons in periodically index-modulated fibers for in-fiber all-optical signal processing.     

The Vlasov-Poisson-Boltzmann System without Angular Cutoff

This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with 3 < γ < ?2s and 1/2 ≤ s < 1, where γ , s are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in Duan et al. (J Diff Eqs 252(12):6356–6386, 2012, Math Models Methods Appl Sci 23(6):927, 2013) for the cutoff kernel with ?2 ≤ γ ≤ 1 to the case ?3 < γ < ?2 as long as the angular singularity exists instead and is strong enough, i.e., s is close to 1. The proof is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in Gressman and Strain (J Amer Math Soc 24(3):771–847, 2011) and the Vlasov-Poisson-Landau system in Guo (J Amer Math Soc 25:759–812, 2012).     

膜截止滤光片的消偏振设计

薄膜截止滤光片在倾斜入射时不可避免地会产生s和 p二个偏振分量的分离,因而在许多应用,特别是光通讯的应用中成为一个棘手的难题。提出了一种新的设计方法,对最常用的45°入射角,实现了长波通和短波通两种截止滤光片的完全消偏振, 在透射率为50%处,其偏振分离分别为0.3 nm和 0.1 nm。基本的设计方法是采用宽带法布里珀罗薄膜干涉滤光片中心波长两侧的干涉带作为长波通或短波通截止滤光片的初始膜系,然后经过适当的优化以提高透射带的透射率。宽带干涉滤光片的间隔层常由半波长厚度的高、低折射率混合膜层组成,如2H2L2H或2L2H2L。由于这种设计的截止区和透射带带宽常嫌不足,故提出了展宽截止区和透射带的方法。对一个典型的短波通截止滤光片,在波长1550 nm,截止区和透射带宽均达到了200 nm。这种设计方法不仅简单、性能优良,而且膜厚控制容差较大,故易于制造。     

薄膜截止滤光片的消偏振设计

薄膜截止滤光片在倾斜入射时不可避免地会产生s和p二个偏振分量的分离,因而在许多应用,特别是光通讯的应用中成为一个棘手的难题。提出了一种新的设计方法,对最常用的45°入射角,实现了长波通和短波通两种截止滤光片的完全消偏振, 在透射率为50%处,其偏振分离分别为0.3 nm和0.1 nm。基本的设计方法是采用宽带法布里珀罗薄膜干涉滤光片中心波长两侧的干涉带作为长波通或短波通截止滤光片的初始膜系,然后经过适当的优化以提高透射带的透射率。宽带干涉滤光片的间隔层常由半波长厚度的高、低折射率混合膜层组成,如2H2L2H或2L2H2L。由于这种设计的截止区和透射带带宽常嫌不足,故提出了展宽截止区和透射带的方法。对一个典型的短波通截止滤光片,在波长1550 nm,截止区和透射带宽均达到了200 nm。这种设计方法不仅简单、性能优良,而且膜厚控制容差较大,故易于制造。     

A Cutoff Waveguide ICRF Coupler for Large Tokamaks

This paper proposes a cutoff waveguide Ion-Cyclotron Range of Frequencies (ICRF) coupler in heatings of fusion plasma for large tokamaks. Structures of tokamaks do not permit enough aperture areas for using cylindrical waveguides in the propagative region. However, if the power source to excite the coupler is located near its aperture, electromagnetic power is expected to pass through the cutoff region as a tunnel effect and radiate into the fusion plasma. We calculate characteristics of the normalized radiation power and the input impedance for this cutoff waveguide coupler, regarding its aperture as a slot. Numerical results show that the cutoff waveguide coupler has a few million watts handling power when the effective dielectric constant of the plasma is between 60 and 100. Experiments for a one-tenth model of actual size are performed using air and water instead of the fusion plasma. Measured input impedance showed a fine agreement with the theory for typical ones. Furthermore, experiments verify that its input impedance can be controlled by the location of a short-circuiting plunger. All these results suggest that the cutoff waveguide coupler is very attractive for ICRF heating.     

Wavelength Extended InGaAsBi Detectors with Temperature-Insensitive Cutoff Wavelength

We demonstrate a wavelength extended InGaAsBi short-wave infrared photodetector on an InP substrate with the 50% cutoff wavelength up to 2.63μm at room temperature. The moderate growth temperature is applied to balance the Bi incorporation and material quality. Photoluminescence and x-ray diffraction reciprocal space mapping measurements reveal the contents of bismuth and indium in InGaAsBi to be about 2.7% and 76%,respectively. The InGaAsBi detector shows the temperature-insensitive cutoff wavelength with a low coefficient of about 0.96 nm/K. The demonstration indicates the InP-based InGaAsBi material is a promising candidate for wavelength extended short-wave infrared detectors working.     

多量子阱光学波导中的模式截止

导出了两种材料构成的多量子阱光波导的模式截止方程，并讨论了Ｓｉ衬底上生长的应变ＧｅｘＳｉ１－ｘ／Ｓｉ多量子阱光波导的模式截止特性。     

Quantum Mechanical Second Virial Coefficient for Cutoff Potentials

The high- and low temperature approximations of the second virial coefficient for cutoff potentials are discussed and compared with numerical results.     

Vacuum Arc Anode Phenomena

This paper briefly reviews anode phenomena in vacuum arcs, specially experimental work. It discusses, in succession, arc modes at the anode, anode temperature measurements, anode ions, transitions of the arc into various modes (principally the anode spot mode), and theoretical explanations of anode phenomena. The two most common anode modes in a vacuum arc are a low current mode where the anode is basically passive, acting only as a collector of particles emitted from the cathode, and a high current mode with a fully developed anode spot. Characteristically this anode spot has a temperature near the atmospheric boiling point of the anode material and is a copious source of vapor and energetic ions. However, other anode modes can exist. A low current vacuum arc with electrodes of readily sputterable material may emit a flux of sputtered atoms from the anode. Usually this sputtered flux will have little effect upon the vacuum arc, but in certain circumstances it could be significant. A vacuum arc doesn't always transfer directly from a low current mode to the anode spot mode. In appropriate experimental conditions, formation of an anode spot may be preceded by the formation of an anode footpoint. This footpoint is luminous, but much cooler than a true anode spot. Finally, (again in appropriate circumstances) several small anode spots may form instead of one large anode spot. With sufficient increase in arc current or arcing time these will usually combine to form a single large active spot.     

High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.