Andrew (Gabriel) Livshits
Effective formation of vortex flow determines the success and effectiveness of many modern industrial processes in which there is a need for a dynamic mix of various liquids and gases
The development of efficient technologies for mechanical processing machines and machining centers with digital control while allowing to drastically reduce costs and significantly improve the quality and accuracy of systems generating eddies, called vortex generators
Besides engineering base for the manufacture of components for the last time scientists from different countries carried out basic and applied research to a better and deeper understanding of the nature of the vortex flow and the top of vortex technology - the nature of the vortex tube
So physicists have created a mathematical model of the motion of curls. The paper was published in the journal Physical Review Letters, its summary can be found on the website of the American Physical Society.
In order to understand the laws of motion of curls, the researchers decided to create a mathematical model based on a simple experiment with a strip of metal.
Strip length of 60 centimeters and a thickness of 0.1 mm was pre-rolled into a coil (quiescent state), and then straightened on the (stress).
After the strip was let go, she folded in a curl. This process, researchers recorded on video and was used for the model.
When the authors were convinced that the model with sufficient accuracy reproduces the behavior of the metal spire, they can conduct virtual experiments with a strip of unlimited length.
Since each segment of the strip in the expanded position contained the same amount of energy, the velocity of the spire was constant.
Growth during the twisting spire was uniformly accelerated and depended only on the time (L = kxt / 3, where t is time).
It was believed that the growth of the size of the curl by bending with time should stop (it should reach a certain natural size).
Actually curl continues to grow regardless of the length of the strip.
This occurs because the force that tries to curl less compensated by the centrifugal force of rotation (gravity in the model did not account for).
Moreover, the increase is self-similar, that is all part of a spring rise proportionally.
What's the shape of the curl commonly found in nature - from the hair to curly tendrils of plants. Some engineers suggest using curls formed with strips of two different materials, as microscopic motors. Work on modeling the movement can help in this engineers.
A huge role in shaping the conditions for the creation of vortex systems play a new composite materials, especially varieties of graphite and its modifications
Since German chemists have created a new material, called airbrushing. A distinctive feature of the new material is extremely low density - less than a microgram per cubic centimeter. Article scientists describing the technology of the new material and some of its properties will appear in the journal Advanced Materials.
The material is a network of carbon nanotubes. To obtain material scientists first produced from zinc oxide based on special technology.
Then, this framework has been placed in a quartz tube in which the high temperature on it was grown airbrush. Scientists have described the relationship among other properties of the material obtained from the parameters that determine its production - such as temperature.
According to the authors, the new material has unique mechanical and electrical properties.
In particular, it can be used to create MEMS devices, as well as the production of electrodes. Especially such material may be required to create tools that have to withstand high acceleration.
The new material is called, by analogy with the air-gel. The name refers to materials whose structure resembles a gel, where the liquid phase is replaced by gas. Such materials, having a very low density, can be with very solid and durable. However, they are almost transparent, what else they are called "solid smoke."
In November 2011, an article in Science, which has been described by way of the production of ultra-light metallic foam. First, scientists have created a polymer base, which does a lot of cylindrical channels. Later on this substrate alloy of nickel and phosphorus. According to the creators, the new material can be used to create a thermal insulation, sound insulation, more efficient electrodes for batteries and more.
Enormous role in the mathematical interpretation of three-dimensional vortex systems have played and the latest developments of mathematicians
Mathematics was first shown an image of a flat torus - abstract mathematical figures, first predicted by mathematicians Nicholas Kuiper and Nobel Laureate John Nash in the middle of the last century. The paper was published in the journal Proceedings of the National Academy of Sciences, its description can be read at the French National Center for Scientific Research.
Flat torus - a figure that is topologically equivalent to a square. If we imagine a square, and connect it to the upper limit of the bottom, we get something like a cylinder. If you then connect the rim with each other, you get a torus - a figure that looks like a donut.
However, if the original square apply vertical and horizontal lines, the vertical lines in the course of the transformation will preserve their length, while the horizontal will be stretched. This is because it is impossible to connect the rim without stretching it.
Nash and Kuiper in the mid fifties, have proved the existence of such a torus in three-dimensional space in which no horizontal or vertical lines are not stretched (in the four-a torus constructed quite simply).
This piece is called a flat torus. Later, in the 70-80's Soviet mathematician Mikhail Gromov has developed a method that could help build such a figure. French mathematicians managed to do on the basis of the Gromov algorithm will get the image shapes.
Algorithm in the following way. He started with the usual smooth torus and crumple it so that the vertical lines of the original square close to the length of a stretched horizontal. This "shrinkage" consistently perform up until the figure did not reach the desired level of detail.
The resulting three-dimensional computer model consisted of nearly two billion nodes. She looked like a torus shape, though, and had unusual properties. The surface of the model was periodic (self-similar), and it looked like a fractal surface, but, unlike fractals, still remained smooth.
To understand what a flat torus, imagine a square in the plane. We assume that the opposite side of the square are identified.
This means that any two-dimensional object on this square, stopping at one end, the opposite leaves (fans of the classic game will remember that in the "asteroid" exactly flying asteroids).
To understand that this is a torus, we glue the two edges of the square - we get a cylinder. Now glue the rim and get all the usual bagel.
In this case, if the bond is actually carried out, would be clear that a paper square cylinder becomes quite simple, but the cylinder torus - no longer exists.
This is due to the fact that in our square segments parallel to the sides have the same length, horizontal and vertical, while at this donut parallel (for example, on the outside and on the inside of the torus) have different lengths.
To make a paper cylinder torus, it will crush, will be kinks, sharp edges, that is, the surface is C1-manifold.
As part of the work published in the journal Proceedings of the National Academy of Sciences, the French scientists have proposed to operate in the following manner.
First they took the normal torus in three-dimensional space, and then began to resent it so that the length of some parallels increased, and the length of the other - is reduced.
Disturbances were divided into a sequence of steps, which limit and had to be the right investment.
In the limit of an object is obtained, which at every point a tangent plane, but to build it like a fractal. These objects scientists named C1-fractals. According to them, these fractals may be of interest to mathematicians theorists.
The construction of an isometric embedding of flat torus interesting, of course, in and of itself - back to the analogy of stealing a purse, always nice to know who was still a thief.
However, the first job, most likely, is only the first sign: now that the French have proven feasibility of the method of convex integration, it will attract the attention of specialists in computational mathematics throughout the world. Who knows, maybe they will receive such a beautiful picture.
The fruit combination and integration technologies - is the many types of vortex generating systems used in various processes of vortex formation, from the system of vortex liquid injection into the gas stream and ending vortex mixing natural gas with air in a variety of industrial thermodynamic systems
The following are some examples of three-dimensional models of such systems, including three-dimensional vortex generators, capable of effectively and developed dynamically generate a vortex tube, traffic flows that fully obeys a modern interpretation of the basic physical laws