Laws of form

Michael Schrage His work is superb. Incidentally, the ideas in A Pattern Language have been reappropriated by the object-oriented software designers (architectural design rules, laws of form, and the like)—truly technology transfer. 

Body plans are the expression of laws of form which organisms cannot change, just as minerals cannot change their crystallisation rules. 

Brown, G. Spenser. Laws of Form. George Allen and Unwin Ltd, London. 1969. 

M. Denton and C. Marshall. Laws of form revisited. Nature, 410 (2001), 417. 

The scaling theory of percolation predicts that the correlation length will obey a scaling law of form [2]... 

One may now consider how changes can be made in a system across an adiabatic wall. The first law of thermodynamics can now be stated as another generalization of experimental observation, but in an unfamiliar form the M/ork required to transform an adiabatic (thermally insulated) system, from a completely specified initial state to a completely specifiedfinal state is independent of the source of the work (mechanical, electrical, etc.) and independent of the nature of the adiabatic path. This is exactly what Joule observed the same amount of work, mechanical or electrical, was always required to bring an adiabatically enclosed volume of water from one temperature 0 to another 02. 

Hooke s law functional form is a reasonable approximation to the shape of the potential gy curve at the bottom of the potential well, at distances that correspond to bonding in md-state molecules. It is less accurate away from equilibrium (Figure 4.5). To model the se curve more accurately, cubic and higher terms can be included and the bond- ching potential can be written as follows ... 

Once the patent appHcation is complete and the inventor has made a formal declaration of inventorship, the appHcation is filed with the U.S. PTO. In the U.S. PTO, the appHcation is the subject of a thorough, formal, and substantive examination by a patent examiner. Once the patent examiner is convinced that the patent appHcation satisfies the statutory requirements provided for under the laws of the United States, the patent appHcation will be allowed to issue as a patent. Issuance takes the form of a pubHcation provided by the U.S. Government. The pubHcation of patents occurs only on Tuesdays that ate not federal hoHdays. At the time of issuance, the patent is assigned a number and made pubHc in a form which allows all interested patties to obtain access to it. 

Because there is no "federal law of trade secrets," protection of trade secrets is often left to the variabHity of the criminal and civil laws of the 50 states. To the extent that a trade secret is property, violation, theft, or misappropriation of the trade secret may be the subject of criminal penalty. To the extent that a trade secret is bound to rights, violation or misappropriation of the trade secret may be the subject of civil penalty. Significant effort, however, has been made in developing a uniform body of law to apply to ideas and innovations which may be the subject of this form of protection. 

Electrolytic Precipitation. In 1800, 31 years before Faraday s fundamental laws of electrolysis, Cmikshank observed that copper metal could be precipitated from its solutions by the current generated from Volta s pile (18). This technique forms the basis for the production of most of the copper and 2inc metal worldwide. 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

The formulation step may result in algebraic equations, difference equations, differential equations, integr equations, or combinations of these. In any event these mathematical models usually arise from statements of physical laws such as the laws of mass and energy conservation in the form. 

When the basic physical laws are expressed in this form, the formulation is greatly facilitated. These expressions are quite often given the names, material balance, energy balance, and so forth. To be a little more specific, one could write the law of conservation of energy in the steady state as... 

The first law of thermodynamics states that energy is conserved that, although it can be altered in form and transferred from one place to another, the total quantity remains constant. Thus, the first law of thermodynamics depends on the concept of energy but, conversely, energy is an essential thermodynamic function because it allows the first law to be formulated. This couphng is characteristic of the primitive concepts of thermodynamics. 

When applied to closed (constant-mass) systems for which the only form of energy that changes is the internal energy, the first law of thermodynamics is expressed mathematically as... 

For a favorable isotherm d n lldc f < 0), Eq. (I6-I3I) gives the impossible result that three concentrations can coexist at one point in the bed (see example below). The correct solution is a shock (or abrupt transition) and not a simple wave. Mathematical theoiy has been developed for this case to give weak solutions to consei vation laws. The form of the solution is... 

In its most simplistic form, Newton s equation of motion (also known as Newton s second law of motion) states that... 

The present author was worried about the lack of knowledge concerning the quality of the kinetic models used in the industry. A model is by definition a small, scaled-down imitation of the real thing. (Men should remember tliis when their mothers-in-law call them model husbands.) In the industry all we require from a kinetic model is that it describe the chemical rate adequately by using traditional mathematical forms (Airhenius law, power law expressions and combinations of these) within the limits of its applications. Neither should it rudely violate the known laws of science. 

Remarks The aim here was not the description of the mechanism of the real methanol synthesis, where CO2 may have a significant role. Here we created the simplest mechanistic scheme requiring only that it should represent the known laws of thermodynamics, kinetics in general, and mathematics in exact form without approximations. This was done for the purpose of testing our own skills in kinetic modeling and reactor design on an exact mathematical description of a reaction rate that does not even invoke the rate-limiting step assumption. 

The removal of heat at a low temperature and its rejeetion at a higher temperature requires work. This is stated simply by the Seeond Law of thermodynamies, one form of whieh is... 

The first law of thermodynamics states that energy cannot be created or destroyed, although it may be changed from one form to another. Stated in equation form, it is written as follows ... 

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