Rigorous treatment of metastable states in the van der Waals-Maxwell theory

We consider a classical system, in a ν-dimensional cube Ω, with pair potential of the formq(r) + γ ^v φ(γr). Dividing Ω into a network of cells ω₁, ω₂,..., we regard the system as in a metastable state if the mean density of particles in each cell lies in a suitable neighborhood of the overall mean densityρ, withρ and the temperature satisfying $$f_0 (\rho ) + \tfrac{1}{2}\alpha \rho ^2 > f(\rho ,0 + )$$ and $$f''_0 (\rho ) + 2\alpha > 0$$ wheref(ρ, 0+) is the Helmholz free energy density (HFED) in the limit γ→ 0; α = ∫ φ(r)d ^v r andf ₀ (ρ) is the HFED for the caseφ = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at timet > 0, given that it satisfied them at time 0, is at mostλt, whereλ is a quantity going to 0 in the limit $$|\Omega | \gg \gamma ^{ - v} \gg |\omega | \gg r_0 \ln |\Omega |$$ Here,r ₀ is a length characterizing the potentialq, andx ? y meansx/y → +∞. For rigid walls, the same result is proved under somewhat more restrictive conditions. It is argued that a system started in the metastable state will behave (over times ?λ ^?1) like a uniform thermodynamic phase with HFED f₀(ρ) + 1/2αρ², but that having once left this metastable state, the system is unlikely to return.     

光学系统的低对比分辨本领和象差的公差

具有大象差的光学系统象差公差问题一直还未得到很好解决。本文中提出以低对比分辨本领作为光学系统的质量指标,并将光学系统的传递函数近似表示为正交多项式之和,象差任意大小的光学系统的最佳校正方案和公差之值就可以求出。在小象差情况下,所得的结果与Strehl判断的结果基本一致。 关键词：     

Frustrations and phase transitions in the three-vertex Potts model with next-nearest-neighbor interactions on a triangular lattice

Phase transitions in two-dimensional arrays described by the three-vertex Potts model involving the interactions between magnetic moments located at the nearest-neighbor and next-nearest-neighbor sites of a triangular lattice are studied using the Monte Carlo method. The ratio of the next-nearest-neighbor and nearest-neighbor exchange constants r = J ₂/J ₁ is chosen within the 0–1 range. The analysis of the low temperature behavior of the entropy and density of states in the system, as well as of the fourth-order Binder cumulants, shows that in the range 0 ≤ r < 0.2, this model exhibits a first-order phase transition, whereas at r ≥ 0.2, frustrations arise in such a system.     

Lattice Boltzmann simulation of 3-dimensional natural convection heat transfer of CuO/water nanofluids

The present study investigated fluid flow and natural convection heat transfer in an enclosure embedded with isothermal cylinder. The purpose was to simulate the three-dimensional natural convection by thermal lattice Boltzmann method based on the D3Q19 model. The effects of suspended nanoparticles on the fluid flow and heat transfer analysis have been investigated for different parameters such as particle volume fraction, particle diameters, and geometry aspect ratio. It is seen that flow behaviors and the average rate of heat transfer in terms of the Nusselt number (Nu) are effectively changed with different controlling parameters such as particle volume fraction (5 % ≤ φ ≤ 10 %), particle diameter (d _p = 10 nm to 30 nm) and aspect ratio (0.5 ≤ AR ≤ 2) with fixed Rayleigh number, Ra = 10⁵. The present results give a good approximation for choosing an effective parameter to design a thermal system.     

Probing PM2.5 with terahertz wave

The goal of continuous ambient participate monitoring has been accomplished by the use of terahertz(THz)wave.The frequency-dependent spectrum and absorbance of the particulate matter(PM2.5)were measured in the range of 0–10 THz.The PM2.5 concentration was calculated according to the sampling time and air flow.With the increase of,the THz wave amplitude gradually decreased and the absorbance A of PM2.5 increased.The relationship between and A can be described mathematically through A0.5.Our results demonstrate that the terahertz wave could be a valuable tool to monitor and inspect the PM2.5 concentration.     

Relationship between corneal and ocular higher order wavefront aberrations and age in children

Purpose

To evaluate the relationship between corneal and ocular higher order wavefront aberrations (HOAs) and age in young subjects aged 20 years or less.

Methods

Corneal and ocular HOAs of the right eyes of 87 normal subjects were measured using videokeratography and the Hartmann–Shack wavefront aberrometer (KR-9000PW; Topcon Corp., Tokyo, Japan). The HOAs were calculated using Zernike polynomials up to the sixth order. From the Zernike coefficients, the root mean squares (RMS) of coma and spherical aberration were calculated.

Results

Corneal spherical-like aberrations significantly correlated with age (r = 0.420, p < 0.001); however, coma-like aberrations and total HOAs did not significantly correlate with age. None of the ocular HOAs significantly correlated with age. In addition, a gender-wise comparison of the collected data showed that corneal and ocular HOAs did not significantly correlate with age.

Conclusion

In children, the corneal and ocular total HOAs did not vary with age. Compared to the previous reports in adults, we found fewer corneal and ocular HOAs in children.

     

直接积分法研究电子光学成像系统的时间像差理论

提出了计算动态电子光学成像系统时间像差系数的新方法——直接积分法.以阴极面逸出的轴向电子初能为ε_z1（0≤ε_z1≤ε_0max）的近轴电子 轨迹为比较 基准,给出了时间像差的定义,详细叙述了直接积分法并给出求解动态电子光学成像系统时 间像差系数的积分表达式.τ变分法求得的二级几何时间像差系数必须求解微分方程, 而直接积分法求得的二级几何时间像差系数全部以积分形式表示,仅需进行积分运算,更适 用于成像系统的实际计算与设计. 关键词： 电子光学成像系统 阴极透镜 动态电子光学 时间像差理论     

High-pressure induced magnetoresistance in <Emphasis Type="Italic">p</Emphasis>-InAs:Mn and <Emphasis Type="Italic">p</Emphasis>-CdGeAs<Subscript>2</Subscript>:Mn

The baric (P ≤ 5GPa) and magnetic-field (H ≤ 5 kOe) dependences of the transverse magnetore-sistance Δρ _xx /ρ₀ have been measured for p-InAs (R _H = 22.5 cm³/C, ρ = 0.15 Ω cm) and the new ferromag-netic semiconductor p-CdGeAs₂ (R _H = 5 cm³/C, ρ = 0.62 Ω cm), doped with a magnetic impurity (Mn), near the temperature T = 297 K. The dependences Δρ _xx /ρ₀ (P, H) for p-InAs:Mn and p-CdGeAs₂:Mn exhibit a magnetoresistive effect with an increase in pressure, and a pressure-induced magnetoresistance hysteresis is observed in p-CdGeAs₂:Mn with a pressure drop.     

光学系统的偏振像差分析

偏振像差是影响光学系统性能的重要因素之一,尤其对偏振有严格要求的光学系统来说更是如此。论述了偏振像差的理论和偏振光线追迹的方法,并对旋转对称光学系统、倾斜偏轴光学系统的偏振像差进行了分析,指出了薄膜设计对偏振像差所产生的重要影响。介绍了提高光学系统偏振精度的几个方法,包括尽可能的减小入射角、薄膜设计的优化和像差之间的相互平衡。     

Modellunabhängige Beschreibung kugelsymmetrischer Ladungsverteilungen bei der Streuung schneller Elektronen an Atomkernen

A method is given to evaluate in a model independent way cross sections for scattering of fast electrons by nuclei. For this purpose the charge distribution in the nucleus will not, as usual, be described by means of the charge densityρ(r), but by the first moment functionT(Q): $$T(Q) = \int\limits_0^Q {r(Q')dQ'} .$$ The integration has to be performed over this part of the charge distribution in which the charge will increase from the value 0 to the valueQ. ThusT(Q) gives the first moment of this part. It will be shown that this function can be fixed by elastic scattering within certain limits.     

Influence of frustrations on the thermodynamic properties of the low-dimensional Potts model studied by computer simulation

Influence of disorder in the form of frustration on the thermodynamic behavior of a two-dimensional three-vertex Potts model has been studied by the Monte Carlo method, taking into account the nearest and next-nearest neighbors. Systems with linear sizes of L × L = N (L = 9–48) on a triangular lattice have been considered. It has been shown that in the case of J₁ > 0 and J₂ < 0 frustrations appear in the spin system within the interval of 0.5 ≤ |r| ≤ 1.0. The model undergoes a phase transition outside this region.     

Stable and Unstable Vortex Knots in a Trapped Bose Condensate

The dynamics of a quantum vortex toric knot T_P,Q and other analogous knots in an atomic Bose condensate at zero temperature in the Thomas–Fermi regime is considered in the hydrodynamic approximation. The condensate has a spatially inhomogeneous equilibrium density profile ρ(z, r) due to the action of an external axisymmetric potential. It is assumed that z_*= 0, r_*= 1 is the point of maximum of function rρ(z, r), so that δ(rρ) ≈ –(α–)z²/2–(α + )(δr)²/2 for small z and δr. The geometrical configuration of a knot in the cylindrical coordinates is determined by a complex 2πP-periodic function A(?, t) = Z(?, t) + i[R(?, t))–1]. When |A| ? 1, the system can be described by relatively simple approximate equations for P rescaled functions \({W_n}(\varphi ) \propto A(2\pi n + \varphi ):i{W_{n,t}} = - ({W_{n,\varphi \varphi }} + \alpha {W_n} - \in W_n^*)/2 - \sum\nolimits_{j \ne n} {1/(W_n^* - W_j^*)} \). For = 0, examples of stable solutions of type W _n = θ _n (?–γt)exp(–iωt) with a nontrivial topology are found numerically for P = 3. In addition, the dynamics of various unsteady knots with P = 3 is modeled, and the tendency to the formation of a singularity over a finite time interval is observed in some cases. For P = 2 and small ≠ 0, configurations of type W₀–W₁ ≈ B₀exp(iζ) + C(B₀, α)exp(–iζ) + D(B₀, α)exp(3iζ), where B₀ > 0 is an arbitrary constant, ζ = k₀?–Ω₀t + ζ0, k₀ = Q/2, and Ω₀ = (–α)/2–2/B₀², which rotate about the z axis, are investigated. Wide stability regions for such solutions are detected in the space of parameters (α, B₀). In unstable zones, a vortex knot may return to a weakly excited state.     

Constraints on the central density and chemical composition of the white dwarf RX J0648.0-4418 with a record period of rotation in a model with the equation of state of an ideal degenerate electron gas

A system of equations and inequalities that allows one to determine the constraints on central density ρ _c and the chemical composition, which is governed by parameter μ _e , of the white dwarf RX J0648.0- 4418 with a record short period of rotation T = 13.18s and mass m = (1.28 ± 0.05)m⊙, has been derived. The analysis of numerical solutions of this system reveal a complex dependence of μ _e on ρ _c . The intervals of variation of μ _e and ρ _c are as follows: 1.09 ≤ μ _e ≤ 1.21 and 9.04 ≤ μ _e /ρ₀ ≤ 10³ (ρ₀ = 0.98 × 10⁶ g/cm³). This range of μ _e values suggests that the white dwarf RX J0648.0-4418 is not made of pure hydrogen and should contain 9–21% of heavy elements. Calculations have been performed with the equation of state of an ideal degenerate electron gas. Approximate analytic expressions (with an accuracy of 10^-3) for the minimum period T _min and mass m of the white dwarf are obtained. It is demonstrated that the white-dwarf mass is almost doubled (compared to the case of no rotation at a fixed central density) as period T approaches T _min.     

The pion pole in hard exclusive vector-meson leptoproduction

Exploiting a set of generalized parton distributions (GPDs) derived from analyses of hard exclusive leptoproduction of ρ ⁰, φ and π ⁺ mesons, we investigate the ω spin density matrix elements (SDMEs) recently measured by the HERMES Collaboration. It turns out, from our study, that the pion pole is an important contribution to ω production. It will be treated as a one-particle exchange since its evaluation from the GPD \(\tilde E\) considerably underestimates its contribution. As an intermediate step of our analysis, we extract the πω transition form factor for photon virtualities less than 4 GeV². From our approach we achieve results for the ω SDMEs in good agreement with the HERMES data. The role of the pion pole in exclusive ρ ⁰ and φ leptoproduction is discussed too.     

Design of Plane-Symmetric Low <Emphasis Type="Italic">F</Emphasis>-number Reflective System Based on Perturbation Aberration Model

All-reflective optical systems have theoretically no chromatic aberration and are suitable for wide spectral application, but co-axial reflective systems are difficult to design as low F-number optical systems. In this paper, the aberration of plane-symmetric optical systems with low F-number is analyzed based on the wavefront derived from optical path length. Up to third-order aberrations are classified into three categories by their characteristics. The reduction method of the dominant aberration, astigmatism-like aberration, is proposed. In the method, the Gauss image plane is modeled by means of a simplified mirror surface with third-order approximation. Because the system is plane-symmetric, symmetric cross section and asymmetric cross section are modelled differently. The design example of a three-mirror system with F/2 is shown.     

Degenerate <Emphasis Type="Italic">r</Emphasis>-Stirling Numbers and <Emphasis Type="Italic">r</Emphasis>-Bell Polynomials

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.     

Revisiting the interacting model of new agegraphic dark energy

In this paper,a new version of the interacting model of new agegraphic dark energy(INADE)is proposed and analyzed in detail.The interaction between dark energy and dark matter is reconsidered.The interaction term Q=bH0ραdeρ1αdm is adopted,which abandons the Hubble expansion rate H and involves bothρde andρdm.Moreover,the new initial condition for the agegraphic dark energy is used,which solves the problem of accommodating baryon matter and radiation in the model.The solution of the model can be given using an iterative algorithm.A concrete example for the calculation of the model is given.Furthermore,the model is constrained by using the combined Planck data(Planck+BAO+SNIa+H0)and the combined WMAP-9 data(WMAP+BAO+SNIa+H0).Three typical cases are considered:(A)Q=bH0ρde,(B)Q=bH0√ρdeρdm,and(C)Q=bH0ρdm,which correspond toα=1,1/2,and 0,respectively.The departures of the models from theΛCDM model are measured by the BIC and AIC values.It is shown that the INADE model is better than the NADE model in the fit,and the INADE(A)model is the best in fitting data among the three cases.     

Colossal room-temperature magnetoresistance in thin La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>y</Subscript>MnO<Subscript>3</Subscript> epitaxial films

The first thin La_1?xAg_yMnO₃ epitaxial films (_y ≤ x) were grown on SrTiO₃ (110) substrates with silver present in the ionized state (Ag⁺) only. The Curie temperatures T_C of the compositions with x = y = 0.05, x = y = 0.1, and x = 0.3 and y = 0.27 crystallizing in the hexagonal structure \(R\bar 3c\) above or close to room temperature. The temperature dependences of electrical resistivity ρ and of magnetoresistance ¦Δρ/ρ/¦ = ¦(ρ_H ? ρ _H = 0)/ρ_H=0¦ pass through maxima near T_C, with the magnetoresistance being negative and reaching colossal values of ～7–20% in a magnetic field H = 8.2 kOe not only at T_C but also at room temperature. The magnetic moment per formula unit as derived from the saturation magnetization at T = 5 K is substantially smaller than expected for complete ferromagnetic ordering. The magnetization in fields of up to 6 kOe depends on the actual sample cooling conditions, and the hysteresis loop of a field-cooled sample is displaced along the H axis by ΔH. The above properties can be accounted for by the fact that the films are in a two-phase magnetic (ferromagnetic-antiferromagnetic) state induced by strong s-d exchange. The maximum value of Δ H was used to calculate the energy of exchange coupling between the ferromagnetic and antiferromagnetic parts of a sample.