Heat and mass transfer in unsaturated porous media at a hot boundary: I. One-dimensional analytical model

We present a model of heat and mass transfer in an unsaturated zone of sand and silty clay soils, taking into account the effects of temperature gradients on the advective flux, and of the enhancement of thermal conduction by the process of latent heat transfer through vapor flow. The motivation for this study is to supply information for the planned storage of thermal energy in unsaturated soils and for hot waste storage. Information is required on the possibility of significant drying at a hot boundary, as this would reduce the thermal conductivity of a layer adjacent to the boundary and, thus, prevent effective heat transfer to the soil. This study indicates the possibility that the considered system may be unstable, with respect to the drying conditions, with the occurrence of drying depending on the initial and the boundary conditions. An analysis performed for certain boundary conditions of heat transfer and for given soil properties, disregarding the advective flux of energy, indicated that there are initial conditions of water content for which heating will not cause significant drying. Under these conditions, fine soils may be better suited for heat transfer at the hot boundary, due to their higher field capacity, although their heat conduction coefficients at saturation are lower than those of sandy soils. At present, these conclusions are limited to the range of 50–80°C. Potential effects of solute concentration at the hot boundary are indicated.     

Saint-Venant's principle in nonlinear plane elasticity with sufficiently small strains

A homogeneous, isotropic cylinder in an equilibrium state of plane strain, whose cross-section is a rectangle R : [0 < y ₁ < 2L; 0 < y ₂ < h] with h/L 1, is considered. There are no body forces and the long sides are stress free. At y ₁ = 0 and y ₁ = 2L, there are arbitrary loadings, each statically equivalent to a uniformly distributed tensile or compressive stress c. Within the theory of nonlinear elasticity and with the strains and strain gradients assumed to be sufficiently small (but with no such assumptions on the displacement gradients), it is proved that if (,=1,2) represents the Cauchy stress tensor and the Kronecker delta, then |–c₁₁| decays exponentially to zero in R with distance from the nearer end, and the decay constant depends only upon the material but is independent of L.     

A simple method for controlled immobilization of proteins on modified SAMs

This paper describes a method for modifying self-assembled monolayers (SAMs) with the nitrilotriacetic acid (NTA) group for subsequent immobilization of hexahistidine tagged proteins. The method has two important improvements over previous ones; firstly it avoids the need to carry out a complex synthesis of the chelator alkanethiols prior to deposition because the reactions are performed in situ on a preassembled SAM. This in situ approach also avoids phase segregation of alkanethiols with different functional groups, especially bulky ones such as NTA and tri(ethylene glycol), since a simple SAM is employed as the starting material. The approach reported here uses mercaptohexadecanoic acid to form a well-ordered homogeneous carboxyl-terminated SAM on a gold surface. The carboxyl group was then condensed with an NTA derivative containing an amino group to form a peptide bond. The product is a surface that, after chelating Ni(2+) ions, binds histidine tagged proteins. The loading of NTA groups can be controlled by choice of reaction conditions thereby removing the need for a second alkanethiol to dilute the surface density of chelator groups and prevent molecular crowding. Both factors allow rapid attainment of optimal protein loading. Fluorescence imaging demonstrated that (His)(6) enhanced green fluorescent protein was reversibly immobilized and importantly, was functional on the surface. Furthermore, data from surface plasmon resonance, cyclic voltammetry and fluorescence spectrometry provided additional information on the specific and reversible immobilization of (His)(6) proteins on the NTA-modified SAM surface.     

Automatic locking of a parametrically resonating,base-excited,nonlinear beam

Nonlinear Dynamics - Described is a closed-loop control scheme capable of stabilizing a parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between...     

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not B _l , l ≥ 3, G ₂ or F ₄. For B _l and F ₄ a close condition turns out to be sufficient. Received: 28 October 2001     

Rectified approximations for the solution of nonlinear equations

In this paper we introduce the ‘rectification method’ for the construction of algorithms of pre-designed order r for the solution of nonlinear equations f(x) = 0. Our method is based upon the derivation of a rectified approximation g(x) to f(x), via Padé formulas, such that the application of the Newton-Raphson iterations to g generates the desired rth order algorithm. Various properties of g are explored as are recursive relations among rectified approximations associated with successive orders of convergence. It is demonstrated that the use of g in favor of f can relax standard sufficient conditions assuring convergence of the iterations.     

Anisotropic percolation and the d-dimensional surface roughening problem

We review recent numerical simulations of several models of interface growth in d-dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent δ=0.63±0.01 (d=1+1) and δ=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. The values of δ in higher dimensions (δ=0.38±0.03 in d=4 and δ=0.27±0.05 in d=5) do not support a recent theoretical conjecture.     

Activation of tertiary paraffins by elemental fluorine

Elemental fluroine was found to substitute, in a regio and stereospecific way, tertiary unactivated hydrogens in alkanes - the most unreactive family of organic compounds.     

The complexity of identifying redundant and essential elements

In many optimization problems a solution is a subset of optimum number of elements satisfying some desired property. An element is redundant if it does not belong to any solution of the problem. An element is essential if it belongs to every solution of the problem. We consider the complexity of indentifying redundant and essential elements in a sample of NP-Hard optimization problems. It is shown that these identification problems are also NP-Hard. The proofs are based on an analysis of the original reductions of Cook [The complexity of theorem proving procedures, in “Proceedings, Third Annual Assoc. Comput. Mach. Symposium on Theory of Computing”, pp. 151–158, Assoc. Comput. Mach., New York 1971] and Karp [Reducibility among combinational problems, in “Complexity of Computer Computations” (R. E. Miller and J. W. Thatcher, Eds.), pp. 85–104, Plenum, New York 1972].