RU2524474C1 - Minimal surface simulation device - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: each housing of a line of housings has the shape of a parallelepiped with top covers. The housings are divided into multiple sections by movable partition walls that are capable of moving in vertical grooves made in side walls of the housings. The outermost partition walls form movable end walls of the housings. The movable partition walls have vertical grooves of a smaller size for flexible inextensible bands. All walls of the housings are transparent. The walls of all adjacent sections have matching valve openings which allow the overflow of liquid in orthogonal directions. Two identical devices are placed over each other and their sections are square-shaped. The bands of the upper and lower devices are arranged orthogonally. Between the bands there are vertical bars of the same size which pass through openings in the top cover of the lower device and in the lower cover of the upper device. Vertical second bars are inserted into the openings of sections of the top cover of the upper device. The first and second bars form common composite vertical bars.

EFFECT: simulation of minimal surfaces.

1 dwg

Description

            Minimum Surface Modeling Device

The invention relates to the field of mechanics and can be used to conduct workshops in physics and mathematics in higher and secondary educational institutions to study the geometric forms of mathematical and physical solutions of isoperimetric problems.

A device is known for modeling a poly-arc [1], designed to represent a sequence of smoothly conjugated, that is, having common tangents at the connection points, for adjacent arcs of circles, possibly of different radii, consisting of a body in the form of a hollow parallelepiped, with a transparent top cover, characterized in that the casing is divided into sections by movable partitions moving in vertical grooves symmetrically located in opposite side walls of the casing, in the end wall and in the movable partitions, t kzhe vertically arranged one groove of smaller size for flexible only in the transverse direction of the belt fixed to the inside of the second end wall. The aim of the invention is to expand the functionality of this device by modeling minimal surfaces.

The technical result that cannot be achieved by any of the known similar technical solutions lies in modeling the minimum surface. The reason for the difficulty of analytical modeling of minimal surfaces is a computationally complex variational problem with many variables that does not currently have an effective solution algorithm.

The specified technical result is achieved by the fact that in the known device for modeling a minimal surface containing a line of cases, each of which has the shape of a parallelepiped, with top covers divided into several sections by movable partitions arranged to move in vertical grooves made in the side walls of the cases, at the same time, the extreme partitions form the movable end walls of the housings; in the movable partitions, smaller grooves are vertically made for flexible inextensible x tapes, all the walls of the housings are made transparent, and in the walls of all adjacent sections there are matching valve openings that allow fluid to flow in orthogonal directions, according to the invention, two identical devices are located one above the other, the sections are made square, while the tapes of the upper and lower devices are located orthogonally, between them vertically mounted rods of the same size passing through the holes in the upper cover of the lower device and in the lower cover of the upper device both planes square sections by touching the corresponding strips of both devices while the top lid in the upper sections of the device the openings are vertically second rod on the upper unit ribbons, wherein the first and second rod form a common component vertical rod.

Figure 1 presents the General structural diagram of the device.

The device consists of a pair of identical devices from the line of cases 1_m each parallelepiped-shaped with top covers 2_mdivided into several square sections 3_mn movable partitions 4_{m.n + 1}moving in vertical grooves 5_mnmade in the side walls of the buildings, the extreme partitions form a movable end wall 6_m and 7_m buildings. In movable partitions 4_{m.n + 1}also smaller grooves 8_{m.n + 1} for flexible inextensible tapes 9_m, collectively taking the target shape of the surface. All walls of the housings are made transparent, and in the walls of all adjacent sections 3_mn matching valve holes 10 are made_2m.2n ,allowing fluid flow in orthogonal directions. Two identical devices are located one above the other, while the tapes of the upper and lower devices are located orthogonally. Between them are mounted vertically rods 11_mn the same size passing through the holes in the upper cover of the lower device and in the lower cover of the upper device of both planes of square sections, touching the respective tapes of both devices. From the upper cover of the upper device from the holes in the sections are mounted vertically rods 12_mnconcerning tapes 9_m the upper device, while the rods 11_mn and 12_mn form a common composite vertical rods.

The device operates as follows. In each of the devices located orthogonally to each other, in the capacity of each section 3_{m.n + 1}divided by tape 9_m, in addition, a viscous incompressible liquid, for example glycerin, is poured in the same proportion for the corresponding sections 3_{m.n + 1}lower and upper devices. Then tape 9_m one of the devices are multidirectionally pulled out of the housings 1_m to stop, with valves 10_2m.2n open for sections 2_{m. *}providing immiscible fluid flow in sections under the tape 9_m and above tape 9_m, and are closed for the walls of sections 3_{* .m + 1} between adjacent tapes 9_mwhile for the second device valves 10_2m.2n open to allow fluid to flow along a number of sections 3_{* .n + 1} crossing tapes 9_m and close for sections 3_{m. *} along tapes 9_m. After the completion of the process, the distribution of liquids inside the devices is the same. Next, the ribbons are pulled 9 _m from another device, providing the opening and closing of valves 10_2m.2n for both devices is similar to the previous process. Repeating these steps many times, alternating stretching tapes 9_m, the steady-state position forms the minimum surface observed by the position of the tops of the rods 12_m in the top device. A variety of minimal surfaces is provided by various fixation of the location of the end movable partitions. The novelty of the invention is due to the originality of the use of poly-arcs for the formation of sections of scalable relief models in the research works of the Institute of Computational Mathematics and Mathematical Geophysics SB RAS [2].

Information sources

1. Kim P.A. DEVICE MODELING OF THE POLIDUK. Patent RU 2461891 C2. Publ. 09/20/2012, bull. N 26.

2. Kim P.A. Polydug as an element for constructing profiles of a scalable terrain model. Tr. Int. scientific Congr. "GEO-Siberia-2007", Novosibirsk, Russia, t.3, p.188-192. 5 pp.

Claims (1)

A minimal surface modeling device comprising a line of housings, each of which is parallelepiped-shaped, with upper covers divided into several sections by movable partitions arranged to move in vertical grooves made in the side walls of the housings, with the extreme partitions forming movable end walls of the housings , in movable partitions vertically smaller grooves are made for flexible inextensible tapes, all the walls of the housings are made transparent, and in the walls all x adjacent sections are made matching valve openings that allow fluid to flow in orthogonal directions, characterized in that two identical devices are located one above the other, the sections are square, while the tapes of the upper and lower devices are arranged orthogonally, the same sized rods are vertically installed between them through the holes in the upper cover of the lower device and in the lower cover of the upper device of both planes of square sections, touching the corresponding flax t of both devices, while in the upper cover of the upper device in the holes of the sections vertically mounted second rods touching the tapes of the upper device, and the first and second rods form a common composite vertical rods.