强磁场下NH4Cl水溶液结构的拉曼光谱研究

迄今为止,国内外存在很多关于强磁场处理对水溶液结构影响的争议,并且关于强磁场对无机盐水溶液结构的研究也相对较少。运用拉曼光谱法,测定了在外加强磁场1.8 T强度下,高纯水与质量分数分别为1%,5%,10%,20%和28%的NH₄Cl水溶液在不同磁化时间下的拉曼散射数据,为拉曼光谱法探究强磁场对水溶液结构的影响提供了一个新的可行方式,丰富了拉曼光谱的研究领域。由实验结果可知,随着磁化时间的增加,水分子中氢键的伸缩振动峰值逐渐升高,经过一定的磁化时间后可以达到饱和。高纯水与不同质量分数的NH₄Cl水溶液的饱和效应时间均不同。高纯水与质量分数为1%,5%,10%,20%和28%的NH₄Cl水溶液峰值饱和时间分别为150,120,120,100,80和80 min。随着NH₄Cl水溶液质量分数的增加,达到磁效应饱和的时间呈现减少的趋势。磁场移除后,测定高纯水与不同质量分数NH₄Cl水溶液的去磁记忆时间。高纯水与质量分数为1%,5%,10%,20%和28%的NH₄Cl水溶液的去磁记忆时间分别为30,40,50,60,80和80 min。随着NH₄Cl水溶液质量分数的增加,去磁记忆时间呈现增加的趋势。利用去卷积拟合的方法对磁化2 h后不同质量分数的NH₄Cl水溶液进行处理。由去卷积拟合结果可知,质量分数为20%的NH₄Cl水溶液比质量分数为10%的NH₄Cl水溶液增加了一个N-H峰,该信号峰随着NH₄Cl水溶液质量分数的增大逐渐增强。DDAA型氢键结构整体上随磁化时间增加而减少,磁化时间的增加对四面体水结构具有破坏作用。当达到饱和磁化时间后,DDAA型氢键不再发生变化。实验结果表明,通过拉曼光谱法可以得到1.8 T强磁场对NH₄Cl水溶液结构的影响规律,为外加强磁场条件下其他无机盐水溶液的研究提供了一定的理论基础。     

Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass

We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable for the case with time-independence mass.     

Exterior and interior metrics with quadrupole moment

We present the Ernst potential and the line element of an exact solution of Einstein’s vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass distribution. We show that in the limiting case of slowly rotating and slightly deformed configuration, there exists a coordinate transformation that relates the exact solution with the approximate Hartle solution. It is shown that this approximate solution can be smoothly matched with an interior perfect fluid solution with physically reasonable properties. This opens the possibility of considering the quadrupole moment as an additional physical degree of freedom that could be used to search for a realistic exact solution, representing both the interior and exterior gravitational field generated by a self-gravitating axisymmetric distribution of mass of perfect fluid in stationary rotation.     

考虑弹簧质量的振子精确解

给出了考虑弹簧质量时弹簧振子系统频率的精确解，指出了近似解的实质是假设弹簧的位移模式为线性模式，而其实解的位移模式为正弦曲线；算例的结果显示，通常情况下，精确解的一阶位移模式与线性模式非常接近，因此近似解具有相当的精度．     

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.     

The virtual mass of an oblate-ellipsoidal bubble

A semi-analytical solution is presented for the virtual mass coefficient of an oblate-ellipsoidal bubble rising in liquid. The solution was found to be a function of Weber number. The present solution compared well with the numerical solution of the lattice Boltzmann method and the analytical solutions of other investigators.     

Mass operator for wave scattering from a slightly random surface

This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures.     

Well-Posedness and Large Time Behaviour for the Non-cutoff Kac Equation with a Gaussian Thermostat

We consider here a Kac equation with a Gaussian thermostat in the case of a non-cutoff cross section. Under the sole assumptions of finite mass and finite energy for the initial data, we prove the existence of a global in time solution for which mass and energy are preserved. Then, via Fourier transform techniques, we show that this solution is smooth, unique and converges to the corresponding stationary state.     

Diffraction and radiation of flexural waves by a circular aperture loaded along the edge

An inhomogeneous wave exponentially decaying in all directions may exist near the edge of a circular aperture if the mass and the moment of inertia are appropriately chosen (i.e., their values coincide with the critical ones) [1]. In this case, the solution to the diffraction problem is not unique. This paper inquires into the feasibility of the solution to the wave diffraction and radiation problem in the case of critical loading. The solution is constructed according to the procedure suggested in [2]. It is shown that the diffraction problem always has a solution while the radiation problem may have no solution. The effects related to the critical mass and the critical moment of inertia do not manifest themselves in the far field.     

On the gravitational field of a mass possessing a magnetic dipole moment

A solution of the Einstein-Maxwell magnetostatic equations describing the gravitational field of a mass endowed with a magnetic dipole moment is presented. It reduces to the Schwarzschild solution if the magnetic field vanishes.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.     

搅拌法制备聚合物微球中油水相对壁厚的影响

为了研究乳液微封装技术中油水相对微球壁厚的影响,推导了在理想状态下微球壁厚、油相质量分数和油水相比这三者之间的函数关系。结果表明:当内相水滴半径和油相质量分数为常数时,微球壁厚是油水相比的单增函数;而当内相水滴半径和油水相比为常数时,微球壁厚是油相质量分数的单增函数。即提高油相质量分数或增大油水相比对增加壁厚而言具有等效性。根据此规律,在搅拌法制备小直径聚苯乙烯微球中,通过调整油水相的各参数,确定了制备小直径厚壁聚苯乙烯微球的关键工艺参数。实验表明:采用搅拌法制备10~25 m壁厚的小直径聚苯乙烯微球时,油相质量分数宜配制为5.3%~7.0%,油水相比宜控制在1.6~2.2之间,而外水相中聚乙烯醇质量分数宜控制在1%~3%之内。     

铜管表面水合物晶体生长特性研究

实验研究了浓度分别为5 wt%、15 wt%、20 wt%、30 wt%的四丁基溴化铵(TBAB)溶液在外径为21mm的铜管外表面的结晶特性.实验首先以15 wt%TBAB溶液为例,观察其降温结晶过程,得到了TBAB水合物晶体在不同阶段生长的特征.然后对不同浓度、不同过冷度条件下的TBAB溶液进行降温结晶实验,观察并测...     

The gravitational field of a homogeneous plate with a non-zero cosmological constant

A static interior solution of Einstein gravitational equations with λ ≠ 0 generated by a plane plate of a constant mass density is found. It is shown how to join this interior solution with the exterior metric as well     

Renormalization of the Mass Gap

We have explicitly shown that QCD is the color gauge invariant theory at non-zero mass gap as well. It has been defined as the value of the regularized full gluon self-energy at some finite point. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.     

A variational principle for black holes

It is shown that the initial data which gives rise to stationary black hole solutions extremizes the mass for a given angular momentum and area of the horizon. The only extremum of the mass for a given area of the horizon but arbitrary angular momentum is the Schwarzschild solution. In this case, and when the angular momentum is small, the extremum of the mass is a local minimum. This suggests that the initial data for the Schwarzschild solution has a smaller mass than any other initial data with the same area of the horizon. If this is the case, there is no possibility of proving the occurrence of naked singularities by methods suggested by Penrose and Gibbons. Together with Carter's theorem, the fact that the extremum is a local minimum indicates that the Kerr solutions are stable against axisymmetric perturbations.     

A Gauss type law for gravity with a cosmological constant

It is shown that Komar's conserved quantities can be generalized to space-times with a cosmological constant in which matter, electric charge, and massless scalar field are sources. In the special case of the Kerr-Newman-de Sitter solution, treated as a solution external to matter sources, these quantities are equal to the global mass and angular momentum of its source. They are determined regardless of any local distribution of the mass and angular momentum of sources in addition to the electric charge given by the classical Gauss' law.     

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.     

The tree graphs of quantum gravity and the Reissner-Nordström solution

It is shown that the manifestly covariant quantization of gravity correctly reproduces the classical Reissner-Nordström solution in the ? → 0 limit. This is explicitly verified by evaluating the lowest order tree graph contribution to the vacuum expectation value of the gravitational field produced by a spherically symmetric c-number charged source. The generalization from a point source to that of finite extension is unavoidable if the ‘trees’ are not to lead to divergent expressions. Moreover, the mass which appears in the R-N solution is seen to be positive definite. For convenience, the source is taken to be a sphere of uniform charge and matter densities. Owing to a mass renormalization relating the total mass of the sphere to its bare mass, charge and invariant extension, both exterior and interior solutions may then be generated. This mass renormalization formula is in complete agreement with that obtained by purely classical reasoning.     

A rotating dust cloud in general relativity II

I give a stationary solution of Einstein's equations representing a rotating cloud of dust. The solution is asymptotically flat, and has no curvature singularities. However, embedded in the cloud is a rotating surface layer of negative mass which precisely cancels the mass of the dust cloud. The solution throws light on the van Stockum class of rotating dust solutions, of which it is a member.