Computation of suboptimal randomized strategies for steering the random motion of a point under partial observation

Consider the random motion in the plane of a pointM, whose velocityv=(v ₁,v ₂) is perturbed by an ²-valued Gaussian white noise. Only noisy nonlinear observations taken on the point location (state) are available toM. The velocityv is of the formv(y)= _u (u ₁,u ₂) _y (du), wherey denotes the value of the observed signal,U is the range of the velocity, and, for eachy, _y is a probability measure on (U). Using the available observations, the pointM wishes to steer itself into a given target set by choosing a randomized strategy ={ _y :y ²}. Sufficient conditions on weak optimal randomized strategies are derived. An algorithm for computing weak suboptimal randomized strategies is suggested, and the strategies are computed for a variety of cases.This work was partially supported by a grant from Control Data.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

Photoinduced electron transfer at liquid|liquid interfaces. Part VII. Correlation between self-organisation and structure of water-soluble photoactive species

The self-organisation of a variety of dyes at the water|1,2-dichloroethane interface was studied by admittance measurements, photocurrent–potential curves and light polarisation anisotropy of the photocurrent. The heterogeneous photo-oxidation of ferrocene was studied at interfaces sensitised by Sn(IV) meso-tetra-(4-carboxyphenyl) porphyrin dichloride (SnTPPC), chlorin e-6, protoporphyrin IX (protoIX) and Fe(III) protoporphyrin IX chloride (Fe-protoIX). Cyclic voltammograms and capacitance voltage curves exhibit different features associated with the self-assembly of the dye species at the liquid|liquid boundary. In the case of SnTPPC, the capacitance curves displayed the characteristic responses commonly associated with the specific adsorption of ionic species. On the other hand, chlorin e-6, protoIX and Fe-protoIX show rather complex behaviour suggesting not only changes in the excess charge but also in the dielectric permittivity of the interface. Differences in the photocurrent efficiency were also observed under the same experimental conditions. The relative magnitude of the photocurrent responses were rationalised in terms of the phenomenological electron transfer rate constant, the photon capture cross-sections and the lifetime of the triplet state as obtained from nanosecond flash photolysis. Finally, the average molecular orientation of the adsorbed photoactive species was estimated from the photocurrent dependence on the angle of light polarisation in total internal reflection. The results show a clear correlation between the orientation of the transition dipole and the distribution of the peripheral carboxyl groups responsible for the hydrophilic nature of the dyes.     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.     

末端碳链长度对偶氮苯自组装膜结构的影响

The end-group dominated molecular orientation in the azobenzene self-assembled monolayers (SAMs), CnAzoC2SH (n=1-4), on gold was evaluated for the first time by grazing incidence reflection absorption FTIR spectroscopy (RA-FTIR). All these azobenzene SAMs have highly-organized and closely-parked structures, with the molecule tilting away gradually from surface normal direction with the increase of end group alkyl length.     

聚(ε-己内酯)薄膜结晶形貌及分子取向研究

用匀胶机通过溶液铸膜方法在硅片和铝箔基板上分别制备具有不同厚度的聚(ε-己内酯)(PCL)薄膜. 通过原子力显微镜(AFM)和偏光衰减全反射傅里叶红外光谱(ATR-FTIR)对薄膜中PCL的结晶形貌、 片晶生长方式及分子链取向进行了研究. AFM结果表明, 在200 nm或更厚的薄膜中, PCL主要以侧立(edge-on)片晶的方式生长; 对于厚度小于200 nm的薄膜, PCL片晶更倾向于以平躺(flat-on)的方式生长. 这种片晶生长方式的改变在硅片和铝箔基板上都表现出同样的倾向. 此外, 在15 nm或更薄的薄膜中, PCL结晶由通常的球晶结构变为树枝状晶体. 偏光ATR-FTIR结果表明, 当膜厚小于200 nm时, 薄膜结晶中PCL分子链沿垂直于基板表面方向取向, 并且膜越薄, 取向程度越高, 与AFM的观测结果一致.     

Random walks on inhomogeneous lattices

For lattices with two kinds of points (black and white), distributed according to a translation-invariant joint probability distribution, we study statistical properties of the sequence of consecutive colors encountered by a random walker moving through the lattice. The probability distribution for the single steps of the walk is considered to be independent of the colors of the points. Several exact results are presented which are valid in any number of dimensions and for arbitrary probability distributions for the coloring of the points and the steps of the walk. They are used to derive a few general properties of random walks on lattices containing traps.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

Novel random poly(propylene isophthalate/adipate) copolyesters: Synthesis and characterization

Poly(propylene adipate) (PPA) and poly(propylene isophthalate/adipate) (PPI-PPA) random copolymers of various compositions were synthesized in bulk and characterized in terms of chemical structure and molecular weight. Furthermore, the thermal behavior was examined by thermogravimetric analysis and differential scanning calorimetry. All the polymers showed a good thermal stability. At room temperature they appeared as semicrystalline materials, except the copolymers containing 20 and 30 mol% of PI units: the main effect of copolymerization was a lowering in the amount of crystallinity and a decrease of melting temperature with respect to homopolymers. The crystalline phase of PPI and PPA was evidenced at high content of propylene isophthalate or propylene adipate units, respectively. Amorphous samples were obtained after melt quenching and an increment of T_g as the content of PI units is increased was observed. This behavior was explained as due to the stiff phenylene groups in the polymeric chain. The Wood equation was found to describe well T_g-composition data. Lastly, the presence of a rigid-amorphous phase was evidenced in the copolymers, differently from PPA homopolymer.