Lincolnshire

Coordinates: 53°4′N 0°11′W / 53.067°N 0.183°W / 53.067; -0.183

Lincolnshire (/ˈlɪŋkənʃər/ or /ˈlɪŋkənʃɪər/; abbreviated Lincs) is a historical county in the east of England. It borders Norfolk to the south east, Cambridgeshire to the south, Rutland to the south west, Leicestershire and Nottinghamshire to the west, South Yorkshire to the northwest, and the East Riding of Yorkshire to the north. It also borders Northamptonshire in the south for just 20 yards (18 m), England's shortest county boundary. The county town is Lincoln, where the county council has its headquarters.

The ceremonial county of Lincolnshire is composed of the non-metropolitan county of Lincolnshire and the area covered by the unitary authorities of North Lincolnshire and North East Lincolnshire. Therefore, part of the ceremonial county is in the Yorkshire and the Humber region of England, and part is in the East Midlands region. The county is the second-largest of the English ceremonial counties and one that is predominantly agricultural in land use. The county is fifth-largest of the two-tier counties, as the unitary authorities of North Lincolnshire and North East Lincolnshire are not included. The county can be broken down into a number of geographical sub-regions including: the Lincolnshire Fens (south-east Lincolnshire), the Carrs (similar to the Fens but in north Lincolnshire), the rolling Chalk hills of the Lincolnshire Wolds, the industrial Humber Estuary and North Sea coast around Grimsby and Scunthorpe, and in the south-west of the county, the Kesteven Uplands, comprising limestone hills in the district of South Kesteven.

Constraint algorithm

In computational chemistry, a constraint algorithm is a method for satisfying a Newtonian motion of a rigid which consists of mass points. By this algorithm, the distance between mass points is maintained constant. In general, the algorithm is constructed by following procedures; (i) choosing novel unconstrained coordinates (internal coordinates), (ii) introducing explicit constraint forces, (iii) minimizing constraint forces implicitly by the technique of Lagrange multipliers or projection methods.

Constraint algorithms are often applied to molecular dynamics simulations. Although such simulations are sometimes performed using internal coordinates that automatically satisfy the bond-length, bond-angle and torsion-angle constraints, simulations may also be performed using explicit or implicit constraint forces for these three constraints. However, explicit constraint forces give a cause of the inefficient computation; more computational power is required to get a trajectory of a given length. Therefore, internal coordinates and implicit-force constraint solvers are generally preferred.