Flow pattern regular expression creating method, regular expression creating apparatus, and computer-executable program

A regular expression creating apparatus that creates a regular expression of a flow pattern in a multiply connected exterior domain with N holes topologically, the apparatus comprising:

• one or more processor devices;
• an interface;
• and
• one or more memory devices connected to the one or more processor devices, the one or more memory devices storing computer readable program instructions that, when executed by the one or more processor devices, cause the one or more processor devices to:
• retrieve one or more flow patterns stored in the one or more memory devices;
• create a graph representation of each of the retrieved one or more flow patterns based on a unique tree being assigned to each field of the retrieved one or more flow pattern, each graph representation having one-to-one correspondence to each of the retrieved one or more flow patterns;
• create a regular expression from each created graph representation;
• store each created regular expression in the one or more memory devices in association with a corresponding one of the retrieved one or more flow patterns;
• receive, from the interface, an instruction to conduct one or more flow pattern calculations,
• retrieve, from the one or memory devices, one or more stored regular expressions for the one or more flow pattern calculations on one or more of the flow patterns associated with the one or more retrieved regular expressions;
• execute the one or more flow pattern calculations based on the one or more retrieved regular expressions;
• and
• output, to the interface, a result of the one or more flow pattern calculations,
• wherein N is an integer equal to or larger than 1,
• wherein each of the one or more flow patterns is defined by at least one of
• 1) a pattern I, among two types of flow patterns that can be topologically adopted in a simply connected exterior domain with a hole, with a 1-source-sink point and two ss-∂-saddle connections,
• 2) a pattern II, among the two types of flow patterns that can be topologically adopted in a simply connected exterior domain with a hole, with a 1-source-sink point, a saddle point, a homoclinic saddle connection connecting to the saddle point, and two ss-saddle connections, and
• 3) a pattern O without any 1-source-sink point in a doubly connected exterior domain with two holes, and
• wherein the flow pattern is a flow pattern diagram that is created by repeating an operation, starting from at least one pattern, of assigning any one of operation words defining five types of operations that can be topologically adopted to add a hole to a flow pattern until a number of holes reaches N.

A non-transitory computer-readable medium comprising computer readable program codes, performed by a regular expression creating apparatus that creates a regular expression of a flow pattern in a multiply connected exterior domain with N holes topologically, the program codes when executed causing a computer to execute:

• retrieving, by one or more processor devices from one or more memory devices of the flow pattern regular expression creating apparatus, one or more flow patterns;
• creating, by the one or more processor devices, a graph representation of each of the retrieved one or more flow patterns based on a unique tree being assigned to each field of the retrieved one or more flow pattern, each graph representation having one-to-one correspondence to each of the retrieved one or more flow patterns;
• creating, by the one or more processor devices, a regular expression from each created graph representation;
• storing, by the one or more processor devices in the one or more memory devices, each created regular expression in association with a corresponding one of the retrieved one or more flow patterns;
• receiving, from an interface, an instruction to conduct one or more flow pattern calculations;
• retrieving, by the one or more processor devices from the one or more memory devices, one or more stored regular expressions for the one or more flow pattern calculations on one or more of the flow patterns associated with the one or more retrieved regular expressions;
• executing by the one or more processor devices, the one or more flow pattern calculations based on the one or more retrieved regular expressions;
• and
• outputting, to the interface, a result of the one or more flow pattern calculations,
• wherein N is an integer equal to or larger than 1,
• wherein each of the one or more flow patterns is defined by at least one of
• 1) a pattern I, among two types of flow patterns that can be topologically adopted in a simply connected exterior domain with a hole, with a 1-source-sink point and two ss-∂-saddle connections,
• 2) a pattern II, among the two types of flow patterns that can be topologically adopted in a simply connected exterior domain with a hole, with a 1-source-sink point, a saddle point, a homoclinic saddle connection connecting to the saddle point, and two ss-saddle connections, and
• 3) a pattern O without any 1-source-sink point in a doubly connected exterior domain with two holes, and
• wherein the flow pattern is a flow pattern diagram that is created by repeating an operation, starting from at least one pattern, of assigning any one of operation words defining five types of operations that can be topologically adopted to add a hole to a flow pattern until a number of holes reaches N.