Method, direct

There are several methods for approaching the phase problem. The direct method or brute force approach simply treats the coordinates of the n atoms in the unit cell as 3n unknowns and solves the overdetermined set of nonlinear equations relating the observed intensities 

There are two different methods of surface modification evaluation of inorganic whiskers the direct method and the indirect method. 

The direct method is used to evaluate surface modification results by measuring surface property changes of whiskers before and after modification. 

In actual research, the activation index (H, mass ratio of the floating portion to total samples) is used to evaluate the surface modiflcation results of whiskers (refer to the national standard GB/T 19281-2006). The detection process is as follows. Add a certain amount of modified whiskers into 100 ml of deionized water and let it sit until clear after stirring for 1-2 minutes. Then remove the floating portion on the solution surface and collect the sunken powders at the bottom. The latter are Altered, dried, and weighed and the activation index is calculated using the following equation  

In this formula, H is the activation index (%) m is the total sample (g) m-y is the sample sunken at the bottom (g). 

2 Measurement of Oil Adsorbing Capacity (Refer to GB/T19281-2003 Standard) 

In general, this approach for species-specific identification of bacterial pathogens involves immobilization of single-stranded 

---

The basic data gathering methods are direct methods which allow visual inspection or at least direct measurement of properties, and indirect methods whereby we infer reservoir parameters from a number of measurements taken in a borehole. The main techniques available within these categories are summarised in the following table ... 

Woolfson M M 1987 Direct methods—from birth to maturity Acfa Crystaiiogr.k 4Z 593-612... 

With XRD applied to bulk materials, a detailed structural analysis of atomic positions is rather straightforward and routine for structures that can be quite complex (see chapter B 1.9) direct methods in many cases give good results in a single step, while the resulting atomic positions may be refined by iterative fitting procedures based on simulation of the diffraction process. 

Many experimental methods may be distinguished by whether and how they achieve time resolution—directly or indirectly. Indirect methods avoid the requirement for fast detection methods, either by detemiining relative rates from product yields or by transfonuing from the time axis to another coordinate, for example the distance or flow rate in flow tubes. Direct methods include (laser-) flash photolysis [27], pulse radiolysis [28]... 

A good recent overview of direct methods in given by ... 

Almidf J 1995 Direct methods in electronic structure theory Modern Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) pp 110-51... 

Palzs B, FogarasI G and Pulay P 1998 An efficient direct method for geometry optimization of large molecules J. Chem. Phys. 109 6571... 

Importantly for direct dynamics calculations, analytic gradients for MCSCF methods [124-126] are available in many standard quantum chemistiy packages. This is a big advantage as numerical gradients require many evaluations of the wave function. The evaluation of the non-Hellmann-Feynman forces is the major effort, and requires the solution of what are termed the coupled-perturbed MCSCF (CP-MCSCF) equations. The large memory requirements of these equations can be bypassed if a direct method is used [233]. Modem computer architectures and codes then make the evaluation of first and second derivatives relatively straightforward in this theoretical framework. 

Iterative solution methods are more effective for problems arising in solid mechanics and are not a common feature of the finite element modelling of polymer processes. However, under certain conditions they may provide better computer economy than direct methods. In particular, these methods have an inherent compatibility with algorithms used for parallel processing and hence are potentially more suitable for three-dimensional flow modelling. In this chapter we focus on the direct methods commonly used in flow simulation models. 

More recent determinations of by the more direct method of observing changes in the absorbance of the solution at 290 nm gave values which were not in very good agreement with these earlier ones (10 kjl mol i s i at 4-0, lo-o and 25-0 °C was i6-o, 30-0, and 95-120, respectively). The reaction was first order in the concentration of nitric acid ([HNO3] = 0-04-0-2 mol 1 at 25 ° C) and thus first-order overall. 

Perhaps the most direct method of evaluating microporosity is to fill up the micropores with some suitable adsorbate whilst leaving the mesopores, macropores and external surface free. The use of n-nonane as a preadsorbate was proposed by Gregg and Langford on the basis of earlier work on the adsorption of n-alkanes C, to C, on ammonium phos-phomolybdate, a microporous solid. This work had shown that the rate at... 

Donato, H. Metz, G. A Direct Method for the Propagation of Error Using a Personal Gomputer Spreadsheet Program, ... 

Noncrystalline domains in fibers are not stmctureless, but the stmctural organization of the polymer chains or chain segments is difficult to evaluate, just as it is difficult to evaluate the stmcture of Hquids. No direct methods are available, but various combinations of physicochemical methods such as x-ray diffraction, birefringence, density, mechanical response, and thermal behavior, have been used to deduce physical quantities that can be used to describe the stmcture of the noncrystalline domains. Among these quantities are the amorphous orientation function and the amorphous density, which can be related to some of the important physical properties of fibers. 

A direct method for obtaining a sodium ionomer by polymerizing a mixture of ethylene, sodium methacrylate, and methacrylic acid has been described (30). 

Determination of Lignin Content. Lignin content in plants (wood) is determined by direct or indirect methods (21). The direct method includes measurement of acid-insoluble (ie, Klason) lignin after digesting wood with 72% sulfuric acid to solubilize carbohydrates (22). The Klason lignin contents of representative lignifted materials are shown in Table 2. 

This direct method of preparing organ oHthium compounds is commonly used in commercial processes. 

Although the Ziegler reaction provides a more direct method for produciag primary alcohols, aluminum alkyl chemistry requires special handling and is fairly cosdy. The by-product aluminum salts usuaUy require some treatment for disposal (115). 

Scale control can be achieved through operation of the cooling system at subsaturated conditions or through the use of chemical additives. The most direct method of inhibiting formation of scale deposits is operation at subsaturation conditions, where scale-forming salts are soluble. For some salts, it is sufficient to operate at low cycles of concentration and/or control pH. However, in most cases, high blowdown rates and low pH are required so that solubihties are not exceeded at the heat transfer surface. In addition, it is necessary to maintain precise control of pH and concentration cycles. Minor variations in water chemistry or heat load can result in scaling (Fig. 12). 

Duff, I. S. Direct Methods for Sparse Matrices, Oxford, Charendon Press (1986). 

Elliptic Equations Elhptic equations can be solved with both finite difference and finite element methods. One-dimensional elhptic problems are two-point boundary value problems. Two- and three-dimensional elliptic problems are often solved with iterative methods when the finite difference method is used and direct methods when the finite element method is used. So there are two aspects to consider howthe equations are discretized to form sets of algebraic equations and howthe algebraic equations are then solved. 

The alternating direction method can be used for elhptic problems by using sequences of iteration parameters (Refs. 106 and 221). The method is well suited to transient problems as well. 

To avoid such small time steps, which become smaller as Ax decreases, an implicit method could be used. This leads to large, sparse matrices rather than convenient tridiagonal matrices. These can be solved, but the alternating direction method is also useful (Ref. 221). This reduces a problem on an /i X n grid to a series of 2n one-dimensional problems on an n grid. 

FIG. 18-85 Depth correction factorto he applied to unit areas determined with Wilhelm-Naide and direct methods. Velocity ratio calculated using tangents to settling cun e at a particular settled solids concentration and at start of test. 

Miniaturisation of various devices and systems has become a popular trend in many areas of modern nanotechnology such as microelectronics, optics, etc. In particular, this is very important in creating chemical or electrochemical sensors where the amount of sample required for the analysis is a critical parameter and must be minimized. In this work we will focus on a micrometric channel flow system. We will call such miniaturised flow cells microfluidic systems , i.e. cells with one or more dimensions being of the order of a few microns. Such microfluidic channels have kinetic and analytical properties which can be finely tuned as a function of the hydrodynamic flow. However, presently, there is no simple and direct method to monitor the corresponding flows in. situ. 

There is a direct and an indirect method of measuring specific soil resistivity. The direct method is carried out in the laboratoiy on a soil sample using a soil box as shown in Fig. 3-16. The resistivity of a soil specimen of cross-section, S, and length, I, is measured and the specific resistivity determined ... 

In small-molecule crystallography the phase problem was solved by so-called direct methods (recognized by the award of a Nobel Prize in chemistry to Jerome Karle, US Naval Research Laboratory, Washington, DC, and Herbert Hauptman, the Medical Foundation, Buffalo). For larger molecules, protein aystallographers have stayed at the laboratory bench using a method pioneered by Max Perutz and John Kendrew and their co-workers to circumvent the phase problem. This method, called multiple isomorphous replacement... 

---