Kushelev A., Polischuk S., Nedelko E., Kozhevnikov D., Pisarzhevsky S.
The Nanoworld Laboratory
Scientific-industrial association "Politechnology"
107005, Russia, Moscow, Gospitalniy per., 10,
The Bauman Moscow State Technical University
Address for correspondence: Pisarzhevsky S.,
123007, Russia, Moscow, Khoroshevskoye shosse 13A-2-52
Tel./fax: 7-095-263-6608
http://ftp.decsy.ru/nanoworld/

The conducting, dielectric and semiconducting resonant systems are known. All of them are related to symmetry classes: m (reflection in a plane), 2, 3, 4, 5, 6... (rotation around an axis), i (inversion rotation).

We have discovered that some cult forms are related to the same symmetry classes. The diversity of the cult forms is significantly more rich than the diversity of the forms of resonance systems known to science today.

The resonators of a closed type (for example cylindrical), open type (for example parallel mirrors) and intermediate (semiclosed) type (for example, magnetron) are applied in a microwave technique now.

The majority of the symmetric cult forms corresponds to the class of the resonators of the semiclosed type.

The typical representative of the cult form corresponding to the resonator of the semiclosed type used in a magnetron is the form of the Gothic rosette.

The main indication of the essential quality of the cult form to the class of the resonators of the semiclosed type is the rotation symmetry. Thus it appears that different on the first view classes of the forms – rosettes, crowns, stars, crosses, tridents, lumps, flowers etc. – have identical topology. The difference of these forms has only parametric character. The consequence of the parametric differences is the different frequency range, different quality factor, different density of currents, different voltages and different powers.

The difference of two major classes of resonators having the cult forms consists in following: the forms belonging to the first of them are constructed on a principle of symmetric placing of spiral sites of the conductors and to the second – sites of variable section.

These two classes of the forms are combined by that a helicity and variable section of the conductor are the two varieties of the change of a wave resistance which differ from each other as angular and linear speed accordingly.

We offer to systematize resonators which have the cult forms as follows: the conducting resonators such as magnetron and the dielectric resonators such as resonators of the whispering gallery (fig. 1).

Fig. 1

The conducting resonators such as magnetron can have the order of symmetry of natural numbers. The forms of such resonators correspond to the forms of Gothic rosette for which the order of symmetry can be 3, 4, 5, 6, 8 and more (fig. 1). The resonance properties of such systems are is checked by us for n = 2, 3, 4, 5, 6, 8, 12, 16, 20, 32, 64. We have detected the invariance of the resonance properties to transformations of the form saving a rotation symmetry experimentally. "Turning inside out the n-magnetrons" we have received the stars (fig. 2). The intermediate forms in the "turning inside out" process are the crowns of different height (fig. 3).

Fig. 2

   
Fig. 3

The cult forms of the types of the diamond cutting, the brooches, the beads etc are resonance systems such of the type of the "whispering gallery".

The extended check has shown that the elements of the type of the "magnetron" can form ornaments which are arranged along a straight line or a circle or may fill by itself a plane or a surface of rotation.

The global check of the resonance properties of the cult forms has shown that the absence of a resonance properties for the cult forms is the exception.

The other global coincidence was revealed by us in natural increase of a maximum current, voltage, frequency and as the result of it the multiple increase of the power of resonance systems related to more late architectural styles (in the number:the early Romanic style;the late Romanic style; the Gothic style; the Classical style) (fig. 4).

 
Fig. 4

Any of the investigated forms can be received algorithmically that we realized in the form of the new programming language "Genetics". In this language the form is represented by the sequence of the commands from the finite set:

mxn – to papallel transfer the element (group) on distance n on x;
sxn – symmetrically reflect along an axis x relatively x = 0;
rxn – to turn around of an axis x on an angle n;
pn – to increase in n time;
gn – to group together n of element.
The replacement of the first character on capital means additional duplication.

We offer the new technology of manufacture of dielectric resonators of the special form discovered in the laboratory "Nanoworld". Among these forms it is possible to mark following: the flatsided and the crookedsided figures with axial symmetry. A characteristic representative of the first group is the precision diamond cutting, of the second group – the sphere modulated by the screw spiral.

The equipment for production of new sorts of dielectric resonators distinguished from disk and spherical ones by heightened selectivity and the greater tuning on frequency is created (fig 5).

 
Fig. 5

The dielectric resonators are made of quartz crystals, sapphire, yttrium-luminium garnet, diamond.

Novelty of the offered technology:

1. The machining is conducted by the symmetrically posed tool;
2. The machining is fractally structured;
3. The machining accuracy is gained automatically similarly to a repetitive process;
4. In the machine tool the special sort of feed of the symmetric tool (symmetric feed) is applied.

In the given technology the machine tool for cutting multistart thread on the spherical, ellipsoidal and toroidal surfaces is used.

The prototype is the machine tool for manufacture of hipoid gears. The new machine tool differs by that instead of feed of the tool on a complex trajectory the symmetrically posed tool is applied. In outcome the process of processing becomes similar to iterative calculations.The multiple spot of contact of the tool and the blank reduces to the process of the averaging of is symmetrically made starts of thread. It allows to gain composite surfaces with deviation from theoretically symmetric surface practically up to the sizes of atoms.

The combination of the longitudinal and the rotary feeds allows to reduce specific consumption of materials of the machine tool. The replacement of the frame on suspension also reduces the weight and the vibrations. The multistage optimization has allowed to receive total weight of the machine tool commensurable with weight of a processed detail (difference in times).

The process of machining is practically silent. The capsulation of engines allows to simplify the process of cooling and feeding of an abradant, omitting (dropping) group of machine tools in a bath with an abradant. In some cases all process goes on one grain of an abrasive that simplifies service up to an automatic filling and removal of the portion of an abrasive.

The resonators created on the base of cult forms in the laboratory "Nanoworld" have frequency range 10⁹...10¹¹ Hz, quality factor 10³...0,8·10¹⁰ and selectivity 40 dB relatively parasite resonances.