Mathematical Modeling and Simulation of Antibubble Dynamics

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.     

Triangle Geometry of the Qubit State in the Probability Representation Expressed in Terms of the Triada of Malevich’s Squares

We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining Triada of Malevich’s squares. The three triangle vertices are located on three sides of another equilateral triangle with the sides equal to\( \sqrt{2} \). We demonstrate that the triangle vertices are in one-to-one correspondence with the points inside the Bloch sphere and show that the uncertainty relation for the three probabilities of spin projections +1/2 onto three orthogonal directions has the bound determined by the triangle area introduced. This bound is related to the sum of three Malevich’s square areas where the squares have sides coinciding with the sides of the triangle. We express any evolution of the qubit state as the motion of the three vertices of the triangle introduced and interpret the gates of qubit states as the semigroup symmetry of the Triada of Malevich’s squares. In view of the dynamical semigroup of the qubit-state evolution, we constructed nonlinear representation of the group U(2).     

动态冰浆传热特性的研究

动态冰浆由于具有较强的蓄能和传热能力,日益受到人们的重视。文中建立了动态冰浆传热特性的数理模型,并利用已知的载流溶液和冰晶的物性参数,得到了动态冰浆在水平直管、等热流加热条件下的传热系数,根据计算结果,分析了传热系数随着冰浆浓度的变化的规律和冰浆流速和管径对动态冰浆传热性能的影响。     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

Determination of Easy Axis in a Chemical Ferromagnet, 4-(p-Chlorobenzylideneamino)–TEMPO (TEMPO=2,2,6,6-Tetramethylpiperidin-1-Oxyl)

The trapping sites for muon and muonium in ferromagnetic p-Cl–Ph–CH=N–TEMPO [(4-(p-chlorobenzylideneamino)–TEMPO (TEMPO = 2,6,6-tetramethyl-piperidin-1-yloxyl)] and the hyperfine interaction tensors for these sites are obtained using first-principles Unrestricted Hartree–Fock theory. The calculated hyperfine interactions are used to compare the calculated zero field muon spin rotation (μSR) frequencies for different choices for the easy axis and the observed frequency. It has been concluded that the two trapping centers that can best explain the observed μSR frequency are a trapped singlet muonium near the radical oxygen and a trapped muon site near the chlorine. The direction of the easy axis also is determined to be the b-axis of the monoclinic lattice. This direction for the easy axis is confirmed by determining the direction of the distributed magnetization in the molecular solid which leads to a minimum dipole–dipole interaction energy. The consequences of this agreement for the easy axis direction by two independent procedures are discussed. This revised version was published online in September 2006 with corrections to the Cover Date.     

Crystalline-phase-dependent red emission behaviors of Gd2O3:Eu3+ thin-film phosphors

Gd₂O₃:Eu³⁺ luminescent thin films have been grown on Al₂O₃(0001) substrates using pulsed-laser deposition. The films grown at different deposition conditions showed different crystalline phases, surface morphologies and luminescent characteristics. Both cubic and monoclinic crystalline phases were observed for the Gd₂O₃:Eu³⁺ films, and the crystalline structure and the surface morphology of the films were highly dependent on the oxygen pressure and substrate temperature. The cubic system showed a higher luminescence than the monoclinic system. The luminescence characteristics were strongly influenced by not only the crystalline structure but also the surface morphology of the films. The photoluminescencebrightness data obtained from Gd₂O₃:Eu³⁺ films indicate that Al₂O₃(0001) is a promising substrate for growth of high-quality Gd₂O₃:Eu³⁺ thin-film red phosphor. In particular, the Gd₂O₃:Eu³⁺ films showed a much better photoluminescence behavior than a Y₂O₃:Eu³⁺ films with the same thickness. PACS 78.20.-e; 78.55.-m; 78.66.-w     

k-space inherited parallel acquisition (KIPA): application on dynamic magnetic resonance imaging thermometry

In this study, a novel method for dynamic parallel image acquisition and reconstruction is presented. In this method, called k-space inherited parallel acquisition (KIPA), localized reconstruction coefficients are used to achieve higher reduction factors, and lower noise and artifact levels compared to that of generalized autocalibrating partially parallel acquisition (GRAPPA) reconstruction. In KIPA, the full k-space for the first frame and the partial k-space for later frames are required to reconstruct a whole series of images. Reconstruction coefficients calculated for different segments of k-space from the first frame data set are used to estimate missing k-space lines in corresponding k-space segments of other frames. The local determination of KIPA reconstruction coefficients is essential to adjusting them according to the local signal-to-noise ratio characteristics of k-space data. The proposed algorithm is applicable to dynamic imaging with arbitrary k-space sampling trajectories. Simulations of magnetic resonance thermometry using the KIPA method with a reduction factor of 6 and using dynamic imaging studies of human subjects with reduction factors of 4 and 6 have been performed to prove the feasibility of our method and to show apparent improvement in image quality in comparison with GRAPPA for dynamic imaging.     

分离式螺旋热管蓄冰过程动态特性模拟

在提出分离式螺旋热管蓄冷空调系统的基础上,建立了螺旋热管蒸发段蓄冰过程的理论模型,分析了单位时间内管外结冰厚度、管外冰层厚度、蓄冰率、单位时间蓄冷量以及系统总蓄冷量随时间的变化关系,并对三种不同管径的螺旋热管的蓄冰特性进行了分析研究,研究结果表明在螺旋热管曲率半径相同的条件下,增大管径可以提高系统的单位时间蓄冷量。     

多波长啁啾叠栅的矩阵分析

在分析多波长啁啾叠栅特征的基础上,提出了多波长啁啾叠栅的矩阵分析模型,采用矩阵分析模型对4波长和8波长啁啾叠栅的反射谱特性进行了理论分析,数值分析结果与实验结果非常一致.还首次数值模拟了波长间隔0.8 nm的16波长啁啾叠栅.此方法对多波长啁啾叠栅的设计和制作具有参考价值.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.