Thermodynamic theory of the Tolman's length

There still exists controversy on the sign and magnitude of the Tolman's length and the Tolman's gap. Further experimental, computational and theoretical investigations on them are needed to solve this problem. In 2006, Blokhuis and Kuipers obtained a rigorous relationship between the Tolman's length and other thermodynamic quantities for the single-component liquid-vapour system. In the present paper, we derive two general relationships between the Tolman's length and other thermodynamic quantities for the single-component liquid vapour system. The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

The new concepts and new developments in hte theory of polymer crystallization

Recently a debate about the initial crystallization process which has not been the hotspot for a long time since the theory proposed by Hoffman- Lauritzen (LH) dominated the field arose again. For a long time the Hoffman-Lauritzen model was always confronted by criticism,and some of the points were taken up and led to modifications, but the foundation remained unchanged which deemed that before the nucleation and crystallization the system was uniform. In this article the classical nucleation and growth theory of polymer crystallization was reviewed, and the confusion of the explanations to the polymer crystallization phenomenon was pointed out. LH theory assumes that the growth of lamellae is by the direct attachment of chain sequences from the melt onto smooth lateral sides.

THEORY OF STEADY-STATE CURRENT AT MULTIPLE MICROCYLINDER ELECTRODES COUPLED WITH A PARALLEL PLANAR ELECTRODE

A novel device of multiple cylinder microelectrodes coupled with a parallel planar electrode was proposed. The feedback diffusion current at this device was studied using bilinear transformation of coordinates in the diffusion space, where lines of mass flux and equiconcentration are represented by orthogonal circular functions. The derived expression for the steady-state current shows that as the gap between cylindrical microelectrodes and planar electrode diminishes, greatly enhanced currents can be obtained with high signal-to-noise ratio. Other important geometrical parameters such as distance between adjacent microcylinders, cylinder radius, and number of microcylinders were also discussed in detail.

APPLICATION OF ULTRAMICROELECTRODES IN STUDIES OF HOMOGENEOUS CATALYTIC REACTIONS .2. A THEORY OF QUASI-1ST AND 2ND-ORDER HOMOGENEOUS CATALYTIC REACTIONS

The analytical expressions of quasi-first and second order homogeneous catalytic reactions with different diffusion coefficients at ultramicrodisk electrodes under steady state conditions are obtained by using the reaction layer concept. The method of treatment is simple and its physical meaning is clear. The relationship between the diffusion layer, reaction layer, the electrode dimension and the kinetic rate constant at an ultramicroelectrode is discussed and the factor effect on the reaction order is described. The order of a catalytic reaction at an ultramicroelectrode under steady state conditions is related not only to C(Z)*/C(O)* but also to the kinetic rate constant and the dimension of the ultramicroelectrode; thus the order of reaction can be controlled by the dimension of the ultramicroelectrode. The steady state voltammetry of the ultramicroelectrode is one of the most simple methods available to study the kinetics of fast catalytic reactions.

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency omega. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

A semi-analytical theory of coastal upwelling and jet

The general forms of the conservation of momentum, temperature and potential vorticity of coastal ocean are obtained in the x-z plane for the nonlinear ocean circulation of Boussinesq fluid, and a elliptic type partial differential equations of second order are derived. Solution of the partial differential equations are obtained under the conditions that the fluid moves along the topography. The numerical results show that there exist both upwelling and downwelling along coastline that mainly depends on the large scale ocean condition. Numerically results of the upwelling (downwelling), coastal jet and temperature front zone are favorable to the observations.

A Theory of Networks for Appxoimation and Learning

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nolinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the well-known Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods such as Parzen windows and potential functions and to several neural network algorithms, such as Kanerva's associative memory, backpropagation and Kohonen's topology preserving map. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.