Experimental research: are those research that analyze the problems and phenomena according to the experimental method, which is based on the observation and put forward hypotheses and adjust the details to verify their authenticity and presence effectively, scholar adjusts all variables and determines its details to control them while serving his research content and perhaps this is more characteristic of empirical research on the other.

Every science has its fundamentals, principles, concepts and laws formulated in a mathematical forms. These laws are general experimental findings of general applicability such as Coulomb law for electrostatic or primitives or logical instructs.

From the structural point of view every object has its model where it is constructed from basic elements connected to each other. Every element has its unique mathematical description and the interaction between the elements is also governed by their laws.

An example is the electrical circuits composed of elements connected with each other by conducting wires. The description of the elements is known and the whole circuit is governed by Kirchhoff laws which are the laws of continuity and conservation applied to electrical circuits.

Now if one has a circuit intended to perform certain function one builds this circuit and solves it by developing a mathematical model which is a system of equations. By solving these equations one gets the behavior of the circuits.

Then one can experimentally measure the behavior of the circuit and compare the two behaviors, if the deviation is within the expected tolerance then this would be considered a verification of the theory. Otherwise one has to investigate the discrepancy and enhance the physical model till one get satisfactory agreement.

Then in this way one raises the confidence in the theory such that one can use it for design of new circuits without returning often to the experiment which may be very expensive.

One can find a complete suit of mathematical tools called computer aided design for many engineering disciplines of science.

For example in circuit analysis there is the SPICE for example, For electron device analysis, one uses SILVACO TCAD.

The steps of solving for any device or circuit or any object:

- Develop a physical model for the object

- Develop mathematical model describing the object based on the basic laws governing the behavior of this object

- Solve the system of equations for the relevant initial and boundary conditions

- Inspect the solution and verify it

- Vary the object parameters and study the effect of system parameters on its behavior

- Experimentally verify the object

Best wishes

A very good answer, Dr. Abdelhalim Zekri.

Theoretical research: This research, which deals with the scientific aspects, from which a set of laws and theories are obtained. It contributes to the growth of knowledge, serves the studies and establishes a documented ground for applied sciences

Applied research: This research is concerned with practical issues and application of knowledge available to access new knowledge more effective, or to solve the problems of the field and develop methods of work to achieve higher productivity.

Experimental research: are those research that analyze the problems and phenomena according to the experimental method, which is based on the observation and put forward hypotheses and adjust the details to verify their authenticity and presence effectively, scholar adjusts all variables and determines its details to control them while serving his research content and perhaps this is more characteristic of empirical research on the other.

Theory is more important

Abdelhalim Zekry I greatly appreciate the detailed insights. Very thought-provoking points raised.

Just adding some thoughts to the already exposed ones:

I agree with Feynman when he said something like (not literally): "It does not matter who said it or how beautiful its mathematics are, if the model does not fit the experimental evidence, its validity must be questioned".

Nonetheless, there are times in which any experimental validation would be rather prohibitively expensive if not impossible. For this reason many of my colleagues working in computer aided process synthesis and optimisation studies often complain about the likelihood/utility/applicability of their results.

I have worked in both theoretical and experimental research, and undoubtedly both require a dose of discipline, imagination and resilience to make the model sound enough or to find why the Nature often behaves 'mischievously' towards 'ideal generalising models'.

Finally, I must admit I have been always curious about the imaginative capacities of pure theoretical physicists that attempt to elucidate the nature of the indivisible even thought it cannot be actually seen or measured without any trace uncertainty.

It depends on the research topic and discipline.