Global optimization and stochastic differential equations

Let ⁿ be then-dimensional real Euclidean space,x=(x ₁,x ₂, ...,x _n)^{T n} , and letf: ⁿ R be a real-valued function. We consider the problem of finding the global minimizers off. A new method to compute numerically the global minimizers by following the paths of a system of stochastic differential equations is proposed. This method is motivated by quantum mechanics. Some numerical experience on a set of test problems is presented. The method compares favorably with other existing methods for global optimization.This research has been supported by the European Research Office of the US Army under Contract No. DAJA-37-81-C-0740.The third author gratefully acknowledges Prof. A. Rinnooy Kan for bringing to his attention Ref. 4.     

Electron radiation effects on the structure of ultradisperse polytetrafluoroethylene

Electron radiation effects (40 mrad, 70 mrad, and 100 mrad) on the molecular and supramolecular structure and morphology of ultradisperse polytetrafluoroethylene obtained by the thermogas dynamic (TGD) method were studied by IR and EPR spectroscopy, X-ray phase analysis, and atomic force microscopy. Irradiation of ultradisperse powder in air leads to oxidized polymer forms due to the terminal carbonyl groups and stable peroxide radicals that appear in the structure. Fast electron radiation in doses of up to 100 mrad did not change the polymer crystallinity and particle entity, while thin films on the surface of ultradisperse polytetrafluoroethylene powder decomposed.     

一种包覆型聚合物高效液相色谱固定相的制备与评价

当代应用最广的HPLC固定相中,硅胶基质填料化学稳定性较低,并且由于残存硅羟基而表现所谓第二效应,特别使碱性化合物的峰形拖尾;聚合物基质填料虽提高了化学稳定性,没有离子基团,但刚性降低,并且由于溶胀难于进行梯度淋洗;面包覆型聚合物填料则可综合二者的优点,本文对我们制备的这种固定相作初步报道。     

Thermal analysis and X-ray studies of chiral ferroelectric liquid crystalline materials and their binary mixtures

Summary Thermal properties of a homologous series of ferroelectric liquid crystals S-(-)-[4-(2-n-alkoxy-propionyloxy)]biphenyl-4'-[n-alkoxy-(3,5-dimethyl)]benzoate have been investigated by polarizing optical microscopy and differential scanning calorimetry. The mesophases were identified and confirmed by X-ray too. Three binary mixtures were prepared from the individual homologues. In one of the mixtures (Mix1), the ferroelectric SmC* phase has broadened and became enantiotropic. This mesophase remained monotropic in the other two mixtures (Mix2, Mix3). The chiral nematic N* phase did not appear in Mix1, but remained monotropic for the other two mixtures. Two molecular parameters, the layer spacing and the average intermolecular distance have been calculated from the X-ray results for the homologues and their mixtures. An intercalated tail-to-tail packing of molecules was found both in the single compounds and their mixtures resulting in the layer spacing about half of the molecular length of the single compounds.     

Surface chemistry of nanoscale Fe_3O_4 dispersed in magnetic fluids

The interaction between stabilizers and nanoparticles is one of the important factors to prepare stable magnetic fluids. The magnetic nano-size Fe3O4 core with single domain and the average grain size around 8-12 nm were prepared by chemical precipitation method. The O/Fe molar ratio of the particle surface was measured by X-ray photoelectron spectroscopy (XPS). The heat effects of stabilizers ad- sorption on nanoparticles were measured by solution calorimetry. The excess amount of oxygen was possibly the result of the hydroxygen formed on the surface of the nanoparticles. The heat effects showed that compounds containing carboxyl groups can be adsorbed chemically on magnetite by forming chemical bonds. The other stabilizers involving NH-groups, such as polyethylene-imine, can be adsorbed physically. The exothermic value is about half of the former case.     

“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Ward's identity in critical dynamics

We consider the relaxation of an order-parameter fluctuation of wave numberk in a system undergoing a second-order phase transition. In general, close to the critical point, wherek ^{–1 –1} (the correlation length) the relaxation rate has a linear dependence on/k of the form (k, ) = (k, 0)x(1–a/k). In analogy with the use of Ward's identity in elementary particle physics, we show that the numerical coefficienta is readily calculated by means of a mass insertion. We demonstrate, furthermore, that this initial linear drop is the main feature of the full/k dependence of the scaling functionR ^–x (k,), wherex is the dynamic critical exponent andR=(k²+ ²)^1/2 is the distance variable.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.