Posted tagged ‘number’

Red Marbles, Blue Marbles

August 24, 2011

Problem: you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

Solution

Chance! chance is easy if you know how to do the formula. we know that we have two choices to make. first we’ll pick a jar, and each jar will have a 1/2 chance of being picked. then we’ll pick a marble, and depending how we stack the marbles, we’ll have a (# of red marbles in jar)/(# of total marbles in jar) chance of getting a red one.

for example, say we put all the red marbles into JAR A and all the blue ones into JAR B. then our chances for picking a red one are:

1/2 chance we pick JAR A * 50/50 chance we pick a red marble
1/2 chance we pick JAR B * 0/50 chance we pick a red marble

do the math and you get 1/2 chance for a red marble from JAR A and a 0/2 chance for a red marble from JAR B. add ‘em up and you get the result = 1/2 chance for picking a red marble.

think about it for awhile and see if you can figure out the right combination. we had a 50/50 (guaranteed) chance in picking a red marble from JAR A, but we didn’t have to have 50 red marbles in there to guarantee those fantastic odds, did we? we could’ve just left 1 red marble in there and the odds are still 1/1. then we can take all those other marbles and throw them in JAR B to help the odds out there.

let’s look at those chances:

1/2 we pick JAR A * 1/1 we pick a red marble
1/2 we pick JAR B * 49/99 we pick a red marble

do the math and add them up to get 1/2 + 49/198 = 148/198, which is almost 3/4.

we can prove these are the best odds in a somewhat non-formal way as follows. our goal is to maximize the odds of picking a red marble. therefore we can subdivide this goal into maximizing the odds of picking a red marble in JAR A and maximizing the odds of picking a red marble in JAR B. if we do that, then we will have achieved our goal. it is true that by placing more red marbles into a jar we will increase the chances of picking a red marble. it is also true that by reducing the number of blue marbles in a jar we will increase the odds also. we’ve maximized the odds in JAR A since 1/1 is the maximum odds by reducing the number of blue marbles to 0 (the minimum). we’ve also maximized the number of red marbles in JAR B. if we added any more red marbles to JAR B we would have to take them out of JAR A which reduce the odds there to 0 (very bad). if we took any more blue ones out of JAR B we would have to put them inJAR A which reduce the odds there by 50% (very bad).

it wasn’t really a good proof, but QED anyway 😛

METALLURGY

August 23, 2011

Definition:

The Process of producing components from metallic powder parts made by powder metallurgy may contain non-metallic constituents to improve the bonding qualities and properties.

Number and variety of products made by powder metallurgy are continuously increasing:

    1. Tungsten Filaments for Lamps
    2. Contact Point relays
    3. Self lubricating bearings
    4. Cemented carbides for cutting tools etc.

02-PowderManufacturing-metallurgy-particles

 

Characters of Metal Powders:

  • Shape:

It is influenced by the way it’s made. The shape may be spherical (atomization) (Electrolysis) flat or angular (Mechanical crushing). The particle shape influences the flow characteristics of powders.

  • Particle Size (Fineness) and size distribution:

Particle Size and Distribution are important factors which controls the porosity, Compressibility and amount of shrinkage. Proper particle size and size distribution are determined by passing the powder through a standard sieves ranging from 45 to 150 micrometer mesh.

  • Flowability:

The ability of the powders to flow readily and conform to the mould cavity. The flow rate helps to determine to possible production rate.

  • Compressibility:

It’s defines as the volume of initial powder (Powder loosely filled in cavity) to the volume of compact part. Depends on particle shape & size distribution.

  • Apparent Density:

The Apparent density depends on particle size is defined as the ratio of volume to weight of loosely filled mixture.

  • Green strength:

It refer to strength of a compact part prior to sintering. It depends on compressibility and helps to handle the parts during the mass production.

  • Purity:

Impurities affects sintering & Compacting Oxides & Gaseous impurities can be removed from the part during sintering by the use of a reducing atmosphere.

  • Sintering ability:

It is the ability which promotes bonding of particles by the application of heat.

 

Powder Metallurgy Process steps:

 

01-powder-metallurgy-process-step by step


 

01-powder metallurgy processes-mixing-finished product

 

02-finished product 

Manufacture of Metal Powders:

Methods:

  • Mechanical pulverization:

Machining, Drilling or Grinding of metals is used to convert them to powders.

  • Machining:

It Produces coarse particles (Flack form) especially Magnesium powders.

  • Milling or Grinding:

It suitable for brittle materials.

  • Shorting:

The process of dropping molten metal through a Sieve or small orifice in to water. This produces Spherical particles or larger size. Commonly used for metals of low melting point.

03-mechanical pulverization-milling-powder

04-crushing-shredding-conveyors-powder

 

  • Atomizing:

In this molten metal is forced through a nozzle, and a stream of compressed air, stream or Inert gas is directed on it break up into five particles. Powders obtained in irregular in shapes. Atomization commonly used for aluminium, Zinc, Tin, Cadmium and other metals of low melting point.

03-atomization-powder metallurgy

 

  • Electrolytic deposition:

It’s used mainly for producing iron and copper powders. These are dense structure with low apparent density. It consists of depositing metal on cathode plate by conventional electrolysis processes. The Cathode paltes are removed and the deposited powder is scraped off. The powder is wasted, dried, screened & oversized particles are milled or ground for fineness. The powder is further subjected to heat treatment to remove the work hardening effect.

  • Chemical reduction:

It’s used for producing iron, Copper, Tungsten, Molybdenum, Nickel & Cobalt powder process consists of reducing the metal oxides by means of carbon monoxide or Hydrogen. After reduction, the powder is usually ground & Sized.

 

Forming to shape:

    1. The process of mixing the powders is called Blending.
    2. The Loose powders are formed in to shape by compacting.

METALLURGY

August 23, 2011

Definition:

The Process of producing components from metallic powder parts made by powder metallurgy may contain non-metallic constituents to improve the bonding qualities and properties.

Number and variety of products made by powder metallurgy are continuously increasing:

    1. Tungsten Filaments for Lamps
    2. Contact Point relays
    3. Self lubricating bearings
    4. Cemented carbides for cutting tools etc.

02-PowderManufacturing-metallurgy-particles

 

Characters of Metal Powders:

  • Shape:

It is influenced by the way it’s made. The shape may be spherical (atomization) (Electrolysis) flat or angular (Mechanical crushing). The particle shape influences the flow characteristics of powders.

  • Particle Size (Fineness) and size distribution:

Particle Size and Distribution are important factors which controls the porosity, Compressibility and amount of shrinkage. Proper particle size and size distribution are determined by passing the powder through a standard sieves ranging from 45 to 150 micrometer mesh.

  • Flowability:

The ability of the powders to flow readily and conform to the mould cavity. The flow rate helps to determine to possible production rate.

  • Compressibility:

It’s defines as the volume of initial powder (Powder loosely filled in cavity) to the volume of compact part. Depends on particle shape & size distribution.

  • Apparent Density:

The Apparent density depends on particle size is defined as the ratio of volume to weight of loosely filled mixture.

  • Green strength:

It refer to strength of a compact part prior to sintering. It depends on compressibility and helps to handle the parts during the mass production.

  • Purity:

Impurities affects sintering & Compacting Oxides & Gaseous impurities can be removed from the part during sintering by the use of a reducing atmosphere.

  • Sintering ability:

It is the ability which promotes bonding of particles by the application of heat.

 

Powder Metallurgy Process steps:

 

01-powder-metallurgy-process-step by step


 

01-powder metallurgy processes-mixing-finished product

 

02-finished product 

Manufacture of Metal Powders:

Methods:

  • Mechanical pulverization:

Machining, Drilling or Grinding of metals is used to convert them to powders.

  • Machining:

It Produces coarse particles (Flack form) especially Magnesium powders.

  • Milling or Grinding:

It suitable for brittle materials.

  • Shorting:

The process of dropping molten metal through a Sieve or small orifice in to water. This produces Spherical particles or larger size. Commonly used for metals of low melting point.

03-mechanical pulverization-milling-powder

04-crushing-shredding-conveyors-powder

 

  • Atomizing:

In this molten metal is forced through a nozzle, and a stream of compressed air, stream or Inert gas is directed on it break up into five particles. Powders obtained in irregular in shapes. Atomization commonly used for aluminium, Zinc, Tin, Cadmium and other metals of low melting point.

03-atomization-powder metallurgy

 

  • Electrolytic deposition:

It’s used mainly for producing iron and copper powders. These are dense structure with low apparent density. It consists of depositing metal on cathode plate by conventional electrolysis processes. The Cathode paltes are removed and the deposited powder is scraped off. The powder is wasted, dried, screened & oversized particles are milled or ground for fineness. The powder is further subjected to heat treatment to remove the work hardening effect.

  • Chemical reduction:

It’s used for producing iron, Copper, Tungsten, Molybdenum, Nickel & Cobalt powder process consists of reducing the metal oxides by means of carbon monoxide or Hydrogen. After reduction, the powder is usually ground & Sized.

 

Forming to shape:

    1. The process of mixing the powders is called Blending.
    2. The Loose powders are formed in to shape by compacting.

INDUCTIVE CHARGING

August 23, 2011

02-powermat-iphone-4-wireless-battery-charger-wireless charging mat-wireless receiver case-new wireless technology

In the future all electronic devices will be wirelessly powered. Small, battery-powered gadgets make powerful computing portable.

The battery charger should be capable of charging the most common battery types found in portable  devices today.  In addition, the charging  should be  controlled from the base station and a bidirectional communication system between  the pickups  and base  station  should be developed.


Inductive Power Systems:

Inductive Power Transfer (IPT)  refers to the concept of transferring electrical power between two isolated circuits across an air gap.  While based on the work and concepts developed by pioneers such as  Faraday and Ampere, it  is  only recently that IPT has been developed into working systems.

Essentially, an IPT system can be divided into two parts;

  • Primary and
  • Secondary.

The primary side of the system is made up of a resonant power supply and a coil. This power supply produces a high frequency sinusoidal current in the coil.  The secondary side (or ‘pickup’) has a smaller coil, and a converter to produce a DC voltage.

01-ecoupled wirelss charging technology-inductive coupling-keep battery life higher-concept-illustration

Working of Inductive Power Transfer:

In this system communications signals are encoded onto the waveform that provides power to the air gap. Communication from the primary side to the secondary is implemented by switching the power signal at the output of the resonant converter between its normal level  and a lower level which is detectable by the pickup but still provides enough power to control the pickup microcontroller. This process is called Amplitude Shift Keying (ASK). This is achieved by varying the output voltage of the buck converter which provides an input DC voltage to the resonant converter.

01-electric vehicles-charging-batteries-wireless charging of electric cars-Delphi_Witricity_Wireless

Communication from the secondary to the primary is achieved by a process called Load Shift Keying (LSK).  This involves varying the loading on the pickup.   Any load on the pickup will reflect a voltage on the primary circuit proportional to the load.  Therefore a variation in the load on the pickup can be detected by the charging station.

The communications system must provide two discrete levels of voltage reflected onto the primary side,  to represent the on and off states for digital communications. The difference must be easily detected on the primary side to provide a robust communications channel. Signals are decoded by simple filters and comparators which feed a  digital signal to the microcontrollers.

Advantages:

EV wireless charging parking 9-29

IPT has a number of advantages over other power transfer methods  – it is unaffected by dirt, dust, water, or chemicals.  In situations such as coal mining IPT prevents sparks and other hazards.  As the coupling is magnetic, there is no risk of electrocution even when used in high power systems.  This makes IPT very suitable for  transport  systems where vehicles follow a fixed track,  such as  in factory materials handling.

Artificial photosynthesis

August 23, 2011

Artificial photosynthesis is one of the newer ways researchers are exploring to capture the energy of sunlight reaching earth.

01-photosynthetic reaction-receive sunlight as photons-transfer energy to a network of pigment protein complexes

Photosynthesis:

01-Photosynthesis-basics-operation-oxygen release-hydrogen splits


Photosynthesis is the conversion of sunlight, carbon dioxide, and water into usable fuel and it is typically discussed in relation to plants where the fuel is carbohydrates, proteins, and fats. Using only 3 percent of the sunlight that reaches the planet, plants collectively perform massive energy conversions, converting just over 1,100 billion tons of CO2 into food sources for animals every year.

Photovoltaic Technology:

This harnessing of the sun represents a virtually untapped potential for generating energy for human use at a time when efforts to commercialize photovoltaic–cell technology are underway. Using a semiconductor–based system, photovoltaic technology converts sunlight to electricity, but in an expensive and somewhat inefficient manner with notable shortcomings related to energy storage and the dynamics of weather and available sunlight.

Artificial Photosynthesis:

01-photosynthesis system-Artificial Photosynthesis-Artificial Photosynthesis Solar energy to produce hydrogen directly used in fuel cell

Two things occur as plants convert sunlight into energy:

  • Sunlight is harvested using chlorophyll and a collection of proteins and enzymes, and
  • Water molecules are split into hydrogen, electrons, and oxygen.

These electrons and oxygen then turn the CO2 into carbohydrates, after which oxygen is expelled.

Rather than release only oxygen at the end of this reaction, an artificial process designed to produce energy for human use will need to release liquid hydrogen or methanol, which will in turn be used as liquid fuel or channeled into a fuel cell. The processes of producing hydrogen and capturing sunlight are not a problem. The challenge lies in developing a catalyst to split the water molecules and get the electrons that start the chemical process  to produce the hydrogen.

There are a number of promising catalysts available, that, once perfected, could have a profound impact on how we address the energy supply challenge:

  • Manganese directly mimics the biology found in plants.
  • Titanium Dioxide is used in dye-sensitized cell.
  • Cobalt Oxide is very abundant, stable and efficient as a catalyst

Artificial Photosynthesis Operation:

01-artificial Photosynthesis-arrays of microwave coated catalysts-split water to make hydrogen or liquid hydrocarbon fuels

Under the fuel through artificial photosynthesis scenario, nano tubes embedded within a membrane would act like green leaves, using incident solar radiation (H³) to split water molecules (H2O), freeing up electrons and oxygen (O2) that then react with carbon dioxide (CO2) to produce a fuel, shown here as methanol (CH3OH). The result is a renewable green energy source that also helps scrub the atmosphere of excessive carbon dioxide from the burning of fossil fuels.

01-artificial photosynthesis solar collector to energy-concentrated solar radiation- convert photosynthesis to Hydrogen and oxygen

History:

Plants use organic compounds that need to be continuously renewed. Researchers are looking for inorganic compounds that catalyze the needed reactions and are both efficient and widely available.

The research has been significantly boosted by the application of nano technology. It’s a good example of the step wise progress in the scientific world.

Studies earlier in the decade showed that crystals iridium efficiently drove the reduction of CO2, but iridium is extremely rare so technology that required its use would be expensive and could never be used on a large scale.

Cobalt crystals were tried. They worked, and cobalt is widely available, but the original formulations weren’t at all efficient.

Things changed with the introduction of nano technology.

The main point is that this unique approach increasing appears to be feasible. It has the advantage of harnessing solar energy in a form that can be stored and used with greater efficiency than batteries and it is at least carbon neutral.