Home Page Overview Site Map Index Appendix Illustration About Contact Update FAQ



Brain Wave


gradient Gradient is a mathematical concept to measure the change of a scalar function over a specified distance and along a given direction. In physical applications, the scalar function can be chemical concentration (as shown in Figure 01), temperature, pressure, heat, gravitational potential, electrical potential, ... etc. The mathematical formula for change of the scalar function in a particular direction is just the slope of the curve:

where r is the change of distance in the direction n.

Figure 01 Chemical Gradient [view large image]

The gradient of the electric potential defines the electric field:
E = -(dV/dr) n.
In general the formula for change of a scalar function in any direction can be expressed as:

where i, j, and k are unit vectors along the x, y, and z axis respectively. The gradient is positive if the scalar function increases toward the direction of change, and is negative for the reverse. Thus the bacteria in Figure 01 must have equiped with sensor that can discern the positive or negative of the chemical gradient. The gradient of the gravitational or electrical potential is the field, which is equal to the force by multiplying an appropriate coupling conatant. A magnetic gradiometer detects the magnetic gradient; it can be used to locate object under the Earth's surface. While a gravity gradiometer measures gravitational gradient; it can be used as verification tool to check the load inside a container or the war head of a missile etc. The dotted curves around the salamander body in Figure 04 represents the equi-potential contours.

Lithium-ion Battery Lithium Battery Applications Voltage is defined as the difference in the values of the potential between two points. Current will flow across these two points (if the medium is conductive or semi-conductive) until there is no more potential difference. That's why we need to replace battery every now and then or have it recharged (Figure 02a). As shown in the same image on the right, it is the stronger tendency of the cobalt oxide to attract electron that produces the discharge.

Figure 02a Lithium-ion Battery
[view large image]

Figure 02b Lithium-ion Battery Applications [view large image]

Figure 02b shows the prevalent of its applications in modern life. The insert in Figure 02c estimates its share among the other types of battery in 2025.

Lithium Resources Lithium is especially useful in making battery because of its tendency to shed the outermost electron (see insert in Figure 02b). The current products are fluid-based that tends to explode in recharging. A lot of efforts are now invested to produce a safer and better all-solid-state Li-metal battery. More than 50% of the lithium deposit is located in South America. Lot of the salts are in Bolivia, which may earn the country a lot of wealth similar to Saudi Arabia. Anyway, as shown in Figure 02d, there are other choices of material to make rechargeable battery. It lists out the pros and cons for each type. Somehow it seems that lithium-ion batteries will become the most useful in the modern world.

Figure 02c Lithium Resources
[view large image]

In additional to its ubiquitous presence in mobile phones, a lithium-ion cordless chainsaw can do 100 cuts before recharge, without the bothersome electric cord or starting problem for the other types.

Types of Rechargeable Batteries Electricity Fairy Long before the prevalence of electricity in modern time, it was celebrated in 1937 with a 10m x 60m canvas known as "La Fée Électricité" inside "Musée d'Art Moderne" in Paris (see Figure 03, which is divided into 7 sections designated as S1, ... S7 from antique idea up to 1937 technology with all the famous personalities, who had something to do with electricity, and the electric fairy flying over the latest achievement at the end).

Figure 02d Types of Rechargeable Batteries [view large image]

Figure 03 Electric Fairy
S1, S2, S3, S4, S5, S6, S7

Body Electric Biologists have known for more than 200 years that nerve impulses are transmitted electrically. Research on body electric has been revived only recently in the past two decades. Countless studies have since confirmed that externally applied electric fields can affect the behaviour of cultured cells, influencing the way they migrate, develop and grow. Internally generated electric fields (typically between 10 and 100 millivolts per millimetre) are an inevitable product of biological systems. Cell membranes and epithelia routinely pump ions from one side to the other, creating gradients in electrical potential. It is found that the electric fields play a vital role in wound healing and regeneration of body parts in lower animals (Figure 04). It also provides a "spatial cues" to establish the left-right asymmetry in embryonic development. Researches in the last 20 years reveal that the existence of all forms of life depends on bio-electricity (body electric), which had been established 3.5 billion years ago in the very first proto-cell.

Figure 04 Body Electric [view large image]

See next section for more on bio-electricity.

Go to Next Section
 or to Top of Page to Select
 or to Main Menu