Numerical programs

By comparing equations 1-4 and 9-11, one can see a one-to-one correspondence between terms in the mathematical description and the numerical program. The flexibility of TOPAZ derives from the fact that the parameters of equations 9-11 (p, Cp, kx, ky, qg, P, y) can be linear or non-linear functions of spatial coordinates, time, and temperature. 

The input to numerical program ODE and the solution of the six differential equations are shown. 

The above analytic solution has two applications (i) to investigate the concentration evolution under the special conditions given above, and (ii) to check the accuracy of numerical programs. One application is given in Example 2-1. 

This chapter is dedicated to all of you who are committed and dedicated to good old General Working (GW) Basic. Like me, you don t want to change to this complex Windows Visual Basic (VB). I have written numerous programs in the old GW Basic and have produced very user-friendly input-output screens using special, commercially sold software packages. Unfortunately, this is all history and we now apply only VB in the Microsoft Windows environment. 

Because numerous programs are available to pursue atomic-level simulations and docking, we do not review in detail the input parameters of each program here. We instead list the available programs and refer the reader to the manuals of each program for specific details. Additionally, we present the published atomic-level simulation and docking studies on T REL1 to provide the reader with specific examples. 

Program Manager The primary interface to Windows that allows you to organize and execute numerous programs by double-clicking an icon in a single graphical window. 

Dynamical simulated annealing (DSA)177 is a variant of restrained molecular dynamics (RMD).178 There are numerous programs available for performing molecular dynamics (MD) simulations, including GROMOS,178 AMBER,179 CHARMM,180 X-PLOR/CNS,181 and OPLS.182 In MD simulations, Newton s equations of motion are solved for all atoms under the influence of a physical force field ( physical), which for a protein has the form183... 

Determination of the distribution of modes y4(F) and the related distribution of sizes requires inversion of the Laplace transform, which is an ill-defined problem for a limited data set containing any noise. There are some numerical programs (such as CONTIN that attempt to perform this inverse transformation. The resulting distributions do sometimes (but not always) correlate (but not coincide) with the actual distribution of hydrodynamic radii in solution. 

Advances in technology for the delivery of intravenous solutions have allowed medically stable patients who require extended PN therapy to be maintained indefinitely on intravenous nutrition. An increasing concern for cost containment of health care services has fostered use of sophisticated infusion devices to provide PN at home. Numerous programs are now available outside the traditional health care setting to support patients with various long-term or permanent medical conditions. Standards have been developed to promote safe and effective care. Home PN services may be coordinated and administered through a hospital, by a commercially operated corporation, or through a joint venture between the two. 

Detailed discussion of discretization techniques and numerical solution methods is beyond the scope of this book. Numerical methods are discussed in detail by, for example, Finlayson (1980), Davis (1984), and Du Chateau and Zachmann (1989). Summaries of different discretization methods applied in the simulation of chromatography are given by Guiochon, Golshan-Shirazi, and Katti (1994) and Guio-chon and Lin (2003). For an introduction into numerical programming procedures see, for example. Press et al. (2002, http //www.nr.com) or Ferziger (1998). 

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