表面分散过程的分形研究

盐类和氧化物等活性组分在一定条件下,可在高比表面载体上自发分散。研究这些过程对多相催化剂、吸附剂的制备过程理解和控制无疑是重要的。这类分散过程已被系统地研究,并提出了单层分散模型,对CuCl_2/γ-Al_2O_3、HgCl_2/活性炭等多种体系,测定了单层分散阈值。表面化学习惯上理解为就是二维的化学。早在1931年Tayor就指出表面是不均匀的,但这种不均匀性是作为对理想二维表面的修正而引入的,如TLK模型。表面科学的这些基本概念其数学基础是欧基里德几何学,其物理背景是晶体结构,不规则性就是指晶体结     

Topotactic reversible phase transition between room-temperature and a new low-temperature modification in the MCl3(THF)3 system

Both single crystals of VCl₃(THF)₃ as well as isotypic cocrystals of the composition MCl₃(THF)₃, M=Ti/V 1/3, undergo a topotactic reversible phase transition to a hitherto unknown low-temperature modification. The close relationship between this new structure and the room-temperature phase determined by Cottonet al. is discussed from the molecular and the intermolecular point of view: Both modifications are built up by conformationally very similar molecules which change their arrangement during the phase transition. Lattice energy calculations confirm that these two alternative arrangements correspond to minima of almost the same packing energy.Dedicated to Professor Dr. G. E. Herberich on the occasion of his 60th birthday.     

On the structure formation of hydrophobed particles in the boundary layer of water and octane phases

Two-dimensional aggregation of the surface modified glass beads was carried out in the boundary layer of water and octane phases. The effect of particles' hydrophobicity was investigated on the structure of forming aggregates and the growth process. The structure of the aggregates and their growth were characterized by a density function which demonstrates the change of mean particle density as a function of aggregate size. The growth yielded fractal or nonfractal structures in the investigated systems. The fractal structure of the aggregates was observed to be dependent on restructuring processes controlled by the surface properties of the beads.The experimental results are compared with earlier findings for aggregation of hydrophobic beads in the boundary layer of water and air phases.On leave from Loránd Eötvös University, Budapest, Hungary     

High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency

Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fraction0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.     

Some results on the behavior and estimation of the fractal dimensions of distributions on attractors

The strong interest in recent years in analyzing chaotic dynamical systems according to their asymptotic behavior has led to various definitions of fractal dimension and corresponding methods of statistical estimation. In this paper we first provide a rigorous mathematical framework for the study of dimension, focusing on pointwise dimension(x) and the generalized Renyi dimensionsD(q), and give a rigorous proof of inequalities first derived by Grassberger and Procaccia and Hentschel and Procaccia. We then specialize to the problem of statistical estimation of the correlation dimension and information dimension. It has been recognized for some time that the error estimates accompanying the usual procedures (which generally involve least squares methods and nearest neighbor calculations) grossly underestimate the true statistical error involved. In least squares analyses of and we identify sources of error not previously discussed in the literature and address the problem of obtaining accurate error estimates. We then develop an estimation procedure for which corrects for an important bias term (the local measure density) and provides confidence intervals for. The general applicability of this method is illustrated with various numerical examples.     

One-dimensional Ising chain with competing interactions: Exact results and connection with other statistical models

We study the ground state properties of a one-dimensional Ising chain with a nearest-neighbor ferromagnetic interactionJ ₁, and akth neighboranti-ferromagnetic interactionJ _k . WhenJ _k/J₁=–1/k, there exists a highly degenerate ground state with a residual entropy per spin. For the finite chain with free boundary conditions, we calculate the degeneracy of this state exactly, and find that it is proportional to the (N+k–1)th term in a generalized Fibonacci sequence defined by,F _N ^(k) =F _N–1 ^(k) +F _N–k ^(k) . In addition, we show that this one-dimensional model is closely related to the following problems: (a) a fully frustrated two-dimensional Ising system with a periodic arrangement of nearest-neighbor ferro- and antiferromagnetic bonds, (b) close-packing of dimers on a ladder, a 2× strip of the square lattice, and (c) directed self-avoiding walks on finite lattice strips.Work partially supported by grants from AFOSR and ARO.     

Bounds for the fundamental solutions of elliptic and parabolic equations

It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds.     

Dimension polynomials of difference local algebras

We extend the concept of the difference dimension polynomial of a difference field extension to difference local algebras. The main theorem of the paper establishes the existence and form of the dimension polynomial associated with the localization of a finitely generated well-mixed difference algebra at a prime reflexive difference ideal.     

Some Remarks on One-dimensional Functions and Their Riemann–Liouville Fractional Calculus

A one-dimensional continuous function of unbounded variation on [0,1] has been constructed.The length of its graph is infnite,while part of this function displays fractal features.The Box dimension of its Riemann–Liouville fractional integral has been calculated.     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.