Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.     

On reachable set of singularly perturbed differential inclusions and optimal control problems

Asymptotic properties of reachable sets of singularly perturbed differential inclusions are given. Their applications to optimal control problems are also studied     

Quality of random number generators significantly affects results of Monte Carlo simulations for organic and biological systems

We have simulated pure liquid butane, methanol, and hydrated alanine polypeptide with the Monte Carlo technique using three kinds of random number generators (RNG's)—the standard Linear Congruential Generator (LCG), a modification of the LCG with additional randomization used in the BOSS software, and the “Mersenne Twister” generator by Matsumoto and Nishimura. While using the latter two RNG's leads to reasonably similar physical features, the LCG produces significant different results. For the pure fluids, a noticeable expansion occurs. Using the original LCG on butane yields, a molecular volume of 171.4 ų per molecule compared to about 163.6–163.9 ų for the other two generators, a deviation of about 5%. For methanol, the LCG produces an average volume of 86.3 ų per molecule, which is about 24% higher than the 68.8–70.2 ų obtained with the RNG's in BOSS and the generator by Matsumoto and Nishimura. In case of the hydrated tridecaalanine peptide, the volume and energy tend to be noticeably greater with the LCG than with the BOSS (modified LCG) RNG's. For the simulated hydrated extended conformation of tridecaalanine, the difference in volume reached about 87%. The uniformity and periodicity of the generators do not seem to play the crucial role in these phenomena. We conclude that, it is important to test a RNG's by modeling a system such as the pure liquid methanol with a well‐established force field before routinely employing it in Monte Carlo simulations. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Unsteady shrinking sheet with mass transfer in a rotating fluid

In this paper, the problem of unsteady flow induced by a shrinking sheet with mass transfer in a rotating fluid is studied. The transformed boundary layer equations are solved numerically by an implicit finite‐difference scheme known as the Keller‐box method. The influence of rotation, unsteadiness and mass suction parameters on the reduced skin friction coefficients f″(0) and g′(0), as well as the lateral velocity and velocity profiles are presented and discussed in detail. Copyright © 2010 John Wiley & Sons, Ltd.     

Iterative solutions to coupled Sylvester-transpose matrix equations

This note studies the iterative solutions to the coupled Sylvester-transpose matrix equation with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of coupled matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.     

大学物理中几个常见超越方程解的渐近表示

简要介绍了布尔曼一拉格朗日级数,并推出了几个常见超越方程的解的渐近表示.     

Re-entrant Photoinduced Morphological Transformation and Temperature-Dependent Kinetic Products of a Rectangular Amphiphilic Diarylethene Assembly

An amphiphilic rectangular-shaped photochromic diarylethene bearing two hydrophobic alkyl chains and two hydrophilic tri(ethylene glycol) chains was synthesized, and its photoinduced morphological transformation in water was investigated. Two unexpected phenomena were revealed in the course of the experiments: a re-entrant photoinduced macroscopic morphological transformation and temperature-dependent kinetic products of supramolecular assembly. When the pure closed-ring isomer was dispersed in water, a re-entrant photoinduced morphological transformation, that is, a photoinduced transition from the hydrated phase to the dehydrated phase and then back to the hydrated phase, was observed by optical microscopy upon irradiation with green light at 20 °C; this was interpreted by the V-shaped phase diagram of the LCST transition. The aqueous assembly of the pure closed-ring isomer was controlled by changing the temperature; specifically, rapid cooling to 15 and 5 °C gave J and H aggregates, respectively, as the kinetic products. The thermodynamic product at both temperatures was a mixture of mostly H aggregate with a small amount of J aggregate. This behavior was rationalized by the temperature-dependent potential energy surface of the supramolecular assembly.     

On the long-time limit of the Garvin–Alterman–Loewenthal solution for a buried blast load

The Garvin–Alterman–Loewenthal solution refers to the problem of a line blast load suddenly applied in the interior of an elastic half-space. It is expected that the long-time asymptotic limit of this solution should be equal to the solution of a related static problem. This expectation is justified here. First, the solution of the static problem is constructed. Then, the asymptotic limit of the transient problem is found, correcting previously published results.