MATHEMATICAL MODELS FOR GENERATING ELECTRICITY

FROM OCEANIC BODY

AbstractIn this paper we present some mathematical models for

the generation of electrical energy from sea bodies and

thunder strikes.

Pictorial models are presented and their mathematical

analyses are given.

Introduction It is said that for Nigeria to be industrialized, she will

need about 120,000 kilo waltz of electricity as against the

present 3to 5 thousand kilo waltz of electricity generated in

the country.

Thus for a quick industrialization of the country, we would

need to depend on nuclei fusion to be able to generate the

expected 120,000 kilo waltz of electricity.

However, generating electricity from nuclei fusion has the following disadvantages:

•It will place Nigeria at a position of high nuclei risk which could be as a result of earthquake as it happened in Japan and China,

thus leading to problem of nuclei radiation ;

•Terrorist gaining control over such nuclei reactor could hold the

nation to ransom;

•It will aggravate the problem of Global warming if most nations

would have to depend on nuclei fusion for electricity generation.

Consequent upon these and coupled with the quest for

industrialization, we need to think and design modalities for the

generation of the 120,000 kilo waltz of electricity that is needed.

Hence the need for the topic “mathematical models for

generating electricity from oceanic body. “

Generating Electricity From The Sea Wave

Our aim is to be able to control the sea water and wave in a way to optimize

it for electricity generation. But there are some constraints to be considered

before the issues of electricity generation can be possible.

The constraints are;

•The violent nature of the sea;

•The sea coast low level;

•The sandy nature of the sea; and

•The salty nature of the sea.

FIG.1This tower was constructed by solving equation below on the 7 th of February 1887;

FIG.2

FIG.3

FIG.4

FIG.5

FIG.6

FIG.7

FIG.9

FIG.10

FIG.11

FIG.12

Because of the violent nature of the sea, we need to impose a system structure that is

•Controllable

•Admissible

•Observable

An admissible system is one to which corrective measures can be administered.

A controllable system is a system that is

mathematical expressed as

that is a system that is bounded below and above.

If there is a finite time and a control

,the state is said to be controllable at time

, which transfers the state

to the origin at time

if all values of are controllable for all the system is completely controllable.

Observable system: is one that is analytic, that is, its first derivative exists within the

interval.

If by observing the output during the finite time interval

.

the state can be determined, the state is said to be

observable at time

Kalman in 1960 showed that a necessary and sufficient condition for controllability and observability is that the system should be a

nonsingular matrix [2]

This is a system that is subject to us in a way thus successfully bypassing the turbulent and violent nature of the sea.

Another concern is the salty nature of the ocean water.

This can be prevented by coating the propeller with polythene material.

Our intention can be conceptualized as follows;

We want to optimize the ocean →

Optimize electricity generation=

Objective is to generate electricity= (Z)Subject to;•The violent nature of the sea;

•The low land of sea coast;

•The sandy nature of the sea; and

•The salty nature of the sea.

The state variable is the wave of the sea = x(t);

The control variable is the structure that is introduced into the sea to control it flow= u(t)

Let the coefficient of the x(t) and u(t) be and respectively ,such that we 𝛼 𝛾

plot 𝛾 u(t) against 𝛾 x(t) .

Then we can write; 𝛾 x(t) + i 𝛾 u(t) (2)

Multiplying 𝛾 x(t) + i 𝛾 u(t) by its conjugate will give;

It follows that we want to

Thus we now have an optimization problem as;

Subject to;

•The violent nature of the sea;

•The low land of sea coast;

•The sandy nature of the sea; and

•The salty nature of the sea

Analysis of the Control Structure

For us to obtain the control structure and to be able to examine its

functionality (what goes on in the structure), we make use of the finite

element method.

This is because the stiffness matrix is defined in the fluid flow problem

to relate nodal volumetric fluid-flow to nodal potentials, and in structure

problem the stiffness matrix is defined to relate nodal forces to nodal

displacement.

For the discretized structure in Fig.10, we want to derive

the element stiffness matrix and equation by using one

dimensional finite element formulation.

This will enable us to determine;

•the potential at the junctions;

•the velocities in each section of the structure and;

•the volumetric flow rate.

It follows that for a smooth pipe [], the permeability coefficient, .We find that the element stiffness matrices are:

Where the units of are meters for fluid flowing through a structure and is the area of each portion of the discretized structure.

If a structure is discretized into parts then there will be nodal potentials or fluid heads.

The determinant given as

The fluid velocity in element 1 is

The Volumetric flow rates

,

,

…

Generating Electricity From The Sound of The Sea Wave

FIG.13

HOW THE STRUCTURE IN FIG.13 WORKS

(i)The dish receives the sound of the sea wave;(ii) the sound sensitive material receives the sound and amplify it;(iii) a piezoelectric transducer converts the sound signal into an

electrical signal;(iv) an ultrasonic transducer converts the electrical signal into an

ultrasonic sound signal;(v) again the amplified ultrasonic sound signal is converted into an

electric signal via a Piezoelectric transducer(vi)an amplifier that will be able to amplify electrical signal is

needed at this point and the found one is a Biomolecular Transistor called Microtubules (MTs).

MICROTUBULES (MTs):Taxol-stabilized Microtubules (MTs) behave as Biomolecular

Transistors capable of amplifying electrical signal.

We want all these structures to be isomorphic, that is, to hold together as one.

Then we are to invoke an integration such that;

represents the transformer

If the electrical energy is very high, we will nee d to be a step down transformer such that

But if the electrical energy is low, we will need to bust it to the order of our desire such that

Thus (10) becomes;

For a step up case. While (10) becomes

It is obvious that since systems of operations,

can be written as matrices which must be square and all of equal order. This will allow for easy multiplication.

FIG.15

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

If the human’s ears are viewed as 2 cylinders, then the volume of air that goes

into the brain is given as

By also considering air flow to the brain through the noisy as a cylinder the volume of air flow is

Thus the volume of air flow to the brain is

It follows that if one wears an ear piece on the two ears, the air flow is reduced to

This is dangerous to the brain !

And

Generating Electricity From Thunder Strike

Electrons are emitted when there is a thunder strike. To overcome the

problem of electricity generation, it is high time we considered how to

gather the electrons that are emitted. There is an existing technology by

which these electrons can be gathered. This is by using a thunder catcher.

A Mathematical View of Thunder Strike and a Thunder Catcher

In Mathematics, the thunder catcher can be viewed as a point of

convergence because the electrons significantly meet on the thunder catcher.

By using an approximate Mathematical Method, one can represent the pictures of the thunder strikes by graph theory as follows;

(i) Fig.17 and fig. 19 can be represented approximately as binary and ternary trees respectively;

(ii) Fig.18 can be studied using the Scattering velocity or complex system Analysis;

(iii)the Schrodinger Equation for n electrons can be used and it is given as;

According to the data collected in this month of April 2013 in

Ado-Ekiti, there was only one thunder strike in my area as shown

below.14/4/2013 Thunder strike

18/4/2013 lightening but no thunder strike

19/4/2013 no thunder strike

20/4/2013 no thunder strike

25/4/2013 no thunder strike

28/4/2013 no thunder strike

The steps by which electricity from thunder strikes can be generated are as follows;

•first find a means of measuring the electrons emitted when there is a thunder strike;

•we are to make use of some thunder catcher that are connected to some capacitors since capacitors can receive and store electrons,

• if the quantity of electrons trapped by the thunder catcher is

as the capacitors serve as electrons banks, we envisage that the electrons

harvested therein could be stored until the next raining season since

thunder strikes do not always occur every time it rained.