Notat_2007_The-Langevin-and-Generalised-Langevin-Approach-to-the-Dynamics-of

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Notation
The following notation, definitions and symbols have been used throughout this book.
A. POTENTIAL ENERGY FUNCTIONS
Hard Sphere Potential
Lennard-Jones 12-6 (or LJ12-6) potential 
or with a core,
Chandler–Weeks–Andersen (or CWA) potential
or with a core,
where �ij is the well depth, �ij the value of r for which u(r) = 0, r0 is the position of the well,
i.e., uij(r0) = � �ij and dij is the core diameter
Soft-sphere potential
where n is an integer.
u r rij ij� � � �� �4
n� �
� �0, 0r r ij
u r r d r d r rij ij ij ij ij ij ij ij� � �� � �� � � �� �� � � � � � � �4 ,
12 6
0� � � �
� �0, 0r r ij
u r r rij ij ij ij ij� � �� � � � �� � � � � �4 , r r
12 6
0� � � �
u r r d r dij ij ij ij ij ij� � �� � �� � � �� �� � � � � �4
12 6� � �
u r r rij ij ij ij� � �� � � � �� � � �4
12 6� � �
u r r d
r d
( ) ,
0,
� 	 �
� �
xv
B. SYMBOLS USED
A, Aij a scalar
A a vector,
Aij a tensor
A an operator
C. OPERATIONS
A Bij ij� � ���A B A Bij ji ij ji
A B A B A B A Bx x y y z z• � � �
xvi Notation