Simulation of the nonlinear vibration of a string using the Cellular Automata based on the reflection rule

In this study, the nonlinear dynamic responses of a string are simulated using the Cellular Automata method based on the reflection rule. In the case of nonlinear systems, the velocity of wave propagation is not constant and depends on the amplitude. A new treatment of the dynamic time step is proposed for the Cellular Automata method considering the effect of the propagation velocity. As numerical examples, first, the dynamic responses of a string with linear characteristic are simulated using the Cellular Automata method. A typical resonance curve can be obtained. Second, the dynamic responses of a string with nonlinear characteristic are simulated using the proposed method. Some characteristic types of vibration can be obtained. It is concluded that the linear and nonlinear dynamic responses of a string may be obtained by simulation using the Cellular Automata method.     

Rheooptical investigation of the crystallization of poly(ethylene terephthalate) under tensile strain

The crystallization of poly(ethylene terephthalate) under uniaxial tensile strain at different extension rates was investigated with optical polarimetry in a temperature range between the glass-transition temperature and the quiescent crystallization temperature. The evolution of the optical properties of the polymer, including the turbidity, birefringence, and dichroism, were monitored simultaneously with the mechanical parameters. To complete the semicrystalline microstructure characterization of the polymer under strain, an online wide-angle X-ray diffraction (WAXD) technique was used in separate experiments, which were performed under the same thermomechanical conditions. For real-time measurements, a high-energy synchrotron radiation source was used. The optical properties provided information about both the crystalline and amorphous phases, whereas the WAXD patterns essentially gave information about the crystalline phase. The two experimental techniques were then used in a complementary way to characterize the semicrystalline microstructure. Significant deviations from the stress-optical rule were found. This was attributed to both transient effects and the appearance of crystallites, which consisted of highly oriented molecular segments that could contribute to the optical anisotropy but not necessarily to the stress. The behavior of the optical dichroism was found to be qualitatively different from that of the birefringence. The latter monotonically increased with the strain, whereas the former first increased with the strain, passed through a maximum, and then decreased to a steady-state value. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1915–1927, 2004     

Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Comparison of the boundary theory with the contact rule of phase regions and Gupta’s method

The phase boundary theory and the contact rule of phase regions are compared, and some weaknesses of the latter are manifested. The comparison between the Gupta’s method and the boundary theory method for constructing multicomponent isobaric sections is also presented.     

Balanced contributions for TU games with awards and applications

Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.     

Fitting the control parameters of a genetic algorithm: An application to technical trading systems design

This paper studies the problem of how changes in the design of the genetic algorithm (GA) have an effect on the results obtained in real-life applications. In this study, focused on the application of a GA to the tuning of technical trading rules in the context of financial markets, our tentative thesis is that the GA is robust with respect to design changes. The optimization of technical trading systems is a suitable area for the application of the GA metaheuristic, as the complexity of the problem grows exponentially as new technical rules are added to the system and as the answer time is crucial when applying the system to real-time data. Up to now, most of GAs applications to this subject obviated the question of possible “design dependence” in their results. The data we report, based on our experiments, do not allow us to refute the hypothesis of robustness of the GA to design implementation, when applying to technical trading systems tuning.     

Making equation of state models predictive: Part 2: An improved PCP-SAFT equation of state

We use the PCP-SAFT equation of state, which is of the Van der Waals type and has a sound physical basis, to predict mixture properties, such as vapor–liquid and liquid–liquid equilibria, as well as excess enthalpies. We use molecular properties, such as dipole moment, quadrupole moment, polarizability and dispersion interaction coefficients, that have been determined quantum mechanically in Part I of this publication and adjust the remaining three pure compound parameters to pure compound data. We finally present a new combination rule for the dispersion energy parameter ? that is based on the quantum mechanically determined data. The predictions based on quantum mechanically determined pure compound properties along with the new combination rule show an improved performance compared to the original PCP-SAFT combination rule.     

Scale invariance rule in electromagnetic scattering

The volume integral equation formalism is used to prove the scale invariance rule for an arbitrarily sized scatterer with an arbitrary shape, morphology, and orientation. The only assumptions are that the scatterer is made of optically isotropic linear materials and is embedded in a homogeneous, linear, isotropic, and nonabsorbing infinite medium.     

High spin chemistry underlying organic molecular magnetism: Topological symmetry rule as the first principle of spin alignment in organic open-shell systems of π-conjugation and their ions

This review paper deals with an overview of molecule-based magnetism as a rapidly developing interdisciplinary field, topological symmetry rule as the first principle of spin alignment in organic open-shell systems in the ground state, the proposal of organic through-bond 1D and 2D ferro- and superparamagnets and the detection of the first organic high-spin molecule, m-phenylenebis(phenylmethylene) in the quintet ground state (S = 2), followed by extended organic high-spin systems with π-conjugation such as aromatic hydrocarbons having S = 3, 4, 5. The paper also describes a theoretical approach to the understanding of electronic spin structures of organic high-spin molecules by invoking both Heisenberg and Hubbard model Hamiltonians, weakly interacting intramolecular high-spin systems from both experimental and theoretical sides, the spin density distribution of the first organic high-spin molecule in terms of electron- nuclear multiple resonance spectroscopy and the detection and characterization of ionic high-spin hydrocarbons, emphasizing the establishment of high spin chemistry underlying organic molecular magnetism.