Gregynog workshop on Shrinking domains Related Topics
Lead Research Organisation:
Cardiff University
Department Name: Computer Science
Abstract
The Workshop will bring together scientists who work on problems involving differential equations on domains which n a natural way can be decomposed into smaller and simpler subdomains. In addition the domains in some natural way will be allowed to shrink to simple limiting structures.
The specific questions (stated in the Objectives section) will provide details that will be invaluable to the manufacturing process of micro electronics and all the consequences that follow from this.
The specific questions (stated in the Objectives section) will provide details that will be invaluable to the manufacturing process of micro electronics and all the consequences that follow from this.
Planned Impact
The proposed workshop will bring together analysts with expertise in functional analysis, and differential geometry to work on the mathematical issues derived from domain shrinking problems. The focus of the workshop will be on new work and open problems that are specifically stated in the case for support.
Like most research in pure mathematics
the direct benefits are likely to be seen in several years rather than the immediate future. However these benefits could be many in vastly different areas for example the economy, science, health care and many other fields.
As we mentioned elsewhere in the proposal, the conclusion of this research will be vital for the enhancement of the micro-electronic manufacturing process.
This will allow the manufacturing an smaller devices as well as making them in a more cost effective way.
For example the theoretical results from our research will be useful in the manufacturing of a quantum switch. This will be an essential component of any quantum computer that is constructed.
Quantum computation will be a vital tool in the speed up of computations as we reach the limit of what can be achieved by current technology. Fast computing facilitates will men that it is possible to produce better medical imaging devices thus providing early diagnosis of difficult to detect cancers.
On the economic front, the miniaturisation of components will allow the design and manufacture of many new electronic devices, thus contributing to the economy.
The main international scientific and manufacturing competitors are currently Russia, Germany, USA
and France, though Russia is in decline due to emigration of many of its experts. The
UK can therefore reasonably expect to become a world leader in these areas provided it
makes the investments necessary to get mathematicians in the UK, particularly
analysts, to work on these topics.
Like most research in pure mathematics
the direct benefits are likely to be seen in several years rather than the immediate future. However these benefits could be many in vastly different areas for example the economy, science, health care and many other fields.
As we mentioned elsewhere in the proposal, the conclusion of this research will be vital for the enhancement of the micro-electronic manufacturing process.
This will allow the manufacturing an smaller devices as well as making them in a more cost effective way.
For example the theoretical results from our research will be useful in the manufacturing of a quantum switch. This will be an essential component of any quantum computer that is constructed.
Quantum computation will be a vital tool in the speed up of computations as we reach the limit of what can be achieved by current technology. Fast computing facilitates will men that it is possible to produce better medical imaging devices thus providing early diagnosis of difficult to detect cancers.
On the economic front, the miniaturisation of components will allow the design and manufacture of many new electronic devices, thus contributing to the economy.
The main international scientific and manufacturing competitors are currently Russia, Germany, USA
and France, though Russia is in decline due to emigration of many of its experts. The
UK can therefore reasonably expect to become a world leader in these areas provided it
makes the investments necessary to get mathematicians in the UK, particularly
analysts, to work on these topics.
Organisations
People |
ORCID iD |
| B Brown (Principal Investigator) |