Periodic replica

The particles in the central computational box is surrounded by image particles residing in each of the periodic replicas of the central box. The image particles move in exactly the same way as the particles in the central computational box. The periodic boundary conditions are implemented so that when a particle moves out of the central computational box during the course of the simulation, then its periodic image reappears at the opposite side of the central computational box. 

We immediately specialize to a bulk-like situation where the central cell is surrounded by periodic replicas in all three spatial dimensions. In this case, the electrostatic potential is given by ... 

The supercell approach consists of a periodic replica of the defect, which is enclosed in a large nonprimitive unit cell. A pictorial view (in 2-D) of the supercell approach is given in Figure 47, where, by starting from the perfect... 

Crystalline materials are composed of periodic replicas of unit cells. In our case, the unit cell is a parallelepiped defined by the edge vectors ai, aa and aa- The volume of the unit cell is the absolute value of determinant of the lattice matrix A = [ai, 2, 83], which is nonzero, as the column vectors of the matrix are linearly independent. The smallest unit cell is called the primitive cell. The positions of the atoms in the primitive cell form the basis of the crystal. 

Change easily into desired shapes—maintain the shape for a long period Replica of body parts (for making shoes), rehabilitation tools, sport protectors, chairs for physically impaired, helmets, mold for ice sculptures Shape change during use—recovery Tires, belt for Japanese kimono, core materials for shoes, cotton for futon, artificial hair, folding of clothes, car bumpers... 

The binary alloy Ac,j Beg, Cyt-I-Ci) = 1, shall be studied by the means of supercells containing N atoms with periodic boundary conditions. Each site of the cell can be occupied by a A or a B atom. If the chemical occupations are not considered, the lattice described by the sites within the supercell and their periodic replicas is a simple lattice, with one atom per unit cell. Below, it shall referred to as the geometrical lattice . In order to have a theory flexible enough to deal on equal footing both with ordered and disordered alloys, in principle, one should consider all the different alloy configurations that belong to the... 

Figure 5.9 Sketch of the integration path to obtain the excess free energy ofaT-junction. The snapshots illustrate the system configurations atdifferentstagesalongthe path. For clarity, the simulation cell and one periodic replica are depicted. The B-component has been removed, and the A-component is shaded in blue. The interface between A-rich and B-rich regions is shown as red surface. The thermodynamic integration scheme is applied to a melt of symmetric diblock copolymers with...

Figure 2 Snapshot from an MD simulation of a multilamellar liquid crystalline phase DPPC bilayer. Water molecules are colored white, lipid polar groups gray, and lipid hydrocarbon chains black. The central simulation cell containing 64 DPPC and 1792 water molecules, outlined m the upper left portion of the figure, is shown along with seven replicas generated by the periodic boundary conditions. (From Ref. 55.)...

Monodispersed 35 nm colloidal silica spheres were used to template a periodic mesoporous polymer [71]. Divinylbenzene was used to make a cross-linked rigid polymer replica, ethylene glycol dimethacrylate ensured that it was flexible and shrinkable, while mixtures of the two were used to vary the degree of shrinkage. In addition, the mesoporous polymer replicas were themselves... 

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