Stochastic optimization of forward recursive functions

This note solves a finite-horizon stochastic optimization problem with forward recursive criterion through dynamic programming. The forward recursive criterion is wide; it includes additive (discounted), multiplicative (discounted risk-sensitive), minimum and terminal criteria. The basic idea is to apply invariant imbedding method for the stochastic optimization. The method incorporates recursive accumulation process into dynamics by expanding the original state space.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Facilitated sulfate transfer across the nitrobenzene-water interface as mediated by hydrogen-bonding ionophores.

Facilitated SO4(2-) transfers by hydrogen bond-forming ionophores are investigated across the nitrobenzene (NB)-water interface by using polarography with a dropping electrolyte electrode. Bis-thiourea 1, alpha,alpha'-bis(N'-p-nitrophenylthioureylene)-m-xylene, is found to significantly facilitate the transfer of the highly hydrophilic SO4(2-) whereas its counterpart, N-(p-nitrophenyl)-N'-propylthiourea (ionophore 2), cannot. In contrast to the predominant formation of a 1:1 complex with SO4(2-) in the bulk NB phase, the SO4(2-) transfer assisted by 1 is indeed based on the formation of a 1:2 complex between SO4(2-) and ionophore, even under the condition of [SO4(2-)]aq > [1]org. Such an exclusive formation of the 1:2 (SO4(2-) to ionophore) complex at the NB-water interface is not observed with structurally similar bis-thiourea 3, alpha,alpha'-bis(N'-phenylthioureylene)-m-xylene, where p-nitrophenyl moietes of bis-thiourea 1 are simply replaced by phenyl groups. The facilitated transfer of SO4(2-) with bis-thiourea 1 is further compared to that of HPO4(2-) and H2PO4- across the NB-water interface, which was previously shown to be assisted by 1 through the formation of the 1:1 and 2:1 (anion to ionophore) complexes, respectively. On the basis of these examinations, unique binding behaviors of hydrogen bond-forming ionophores at the NB-water interface are discussed, with a view towards development of ionophore-based anion-selective chemical sensors.     

Terahertz time-domain spectra of aromatic carboxylic acids incorporated in nano-sized pores of mesoporous silicate.

Terahertz time-domain spectroscopy (THz-TDS) is used to study the intra- and intermolecular vibrational modes of aromatic carboxylic acids, for example, o-phthalic acid, benzoic acid, and salicylic acid, which form either intra- or intermolecular hydrogen bond(s) in different ways. Incorporating the target molecules in nano-sized spaces in mesoporous silicate (SBA-16) is found to be effective for the separate detection of intramolecular hydrogen bonding modes and intermolecular modes. The results are supported by an analysis of the differences in the peak shifts, which depend on temperature, caused by the different nature of the THz absorption. Raman spectra revealed that incorporating the molecules in the nano-sized pores of SBA-16 slightly changes the molecular structures. In the future, THz-TDS using nanoporous materials will be used to analyze the intra- and intermolecular vibrational modes of molecules with larger hydrogen bonding networks such as proteins or DNA.     

Structural and electronic properties of a new molecular conductor, α-(BEDT-TTF)2CsCd(SCN)4

Structural and electronic properties of a new BEDT-TTF based radical cation salt, α-(BEDT-TTF)₂CsCd(SCN)₄, are presented. In the measurements of the electrical resistivity and the magnetic susceptibility, this new α-type salt shows metallic behavior down to low temperature. Measurements of the resistivity under in-plane c-axial strain reveal a newly observed insulating phase, suggesting that α-(BEDT-TTF)₂CsCd(SCN)₄ is placed near an insulating phase which might have close relationships with a superconducting phase realized in α-type salts.     

Characteristic curved structure derived from collagen-containing tubular giant vesicles under static magnetic field

Collagen-containing tubular giant vesicles (Col–tGVs) under a high static magnetic field were found to constitute characteristic curved structures (e.g. circular, 8-figure, and hairpin-loop), which were sustained by polymerization of collagen units inside the tGV. We ascribed the formation of these structures to the elasticity of the tGV and to the competing diamagnetic anisotropies between collagen and the tGV. These curved structures can be well expressed by the equation of elastica.