Shortcut: UPPER_WALLS

Module	bias
Description	Usage
Defines a wall for the value of one or more collective variables,

Details and examples

Defines a wall for the value of one or more collective variables, which limits the region of the phase space accessible during the simulation.

If the inputs to the arguments are scalars the restraining potential starts acting on the system when the value of the CV is greater than a certain limit $a_i$ (AT) minus an offset $o_i$ (OFFSET). The expression for the bias due to the wall is given by:

$$\sum_i {k_i}((x_i-a_i+o_i)/s_i)^e_i$$

In this expression $k_i$ (KAPPA) is an energy constant in internal unit of the code, $s_i$ (EPS) a rescaling factor and $e_i$ (EXP) the exponent determining the power law. By default: EXP = 2, EPS = 1.0, OFFSET = 0.

The following input tells plumed to add both a lower and an upper walls on the distance between atoms 3 and 5 and the distance between atoms 2 and 4. The lower and upper limits are defined at different values. The strength of the walls is the same for the four cases. It also tells plumed to print the energy of the walls.

Click on the labels of the actions for more information on what each action computes

d1The DISTANCE action with label d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
d1
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=3,5
d2The DISTANCE action with label d2 calculates the following quantities:
 Quantity   
 Type   
 Description  
d2
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=2,4
uwallThe UPPER_WALLS action with label uwall calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall.bias
scalar
the instantaneous value of the bias potential
uwall.force2
scalar
the instantaneous value of the squared force due to this bias potential: UPPER_WALLSDefines a wall for the value of one or more collective variables, More details ARGthe arguments on which the bias is acting=d1,d2 ATthe positions of the wall=1.0,1.5 KAPPAthe force constant for the wall=150.0,150.0 EXP the powers for the walls=2,2 EPS the values for s_i in the expression for a wall=1,1 OFFSET the offset for the start of the wall=0,0
lwallThe LOWER_WALLS action with label lwall calculates the following quantities:
 Quantity   
 Type   
 Description  
lwall.bias
scalar
the instantaneous value of the bias potential
lwall.force2
scalar
the instantaneous value of the squared force due to this bias potential: LOWER_WALLSDefines a wall for the value of one or more collective variables, More details ARGthe arguments on which the bias is acting=d1,d2 ATthe positions of the wall=0.0,1.0 KAPPAthe force constant for the wall=150.0,150.0 EXP the powers for the walls=2,2 EPS the values for s_i in the expression for a wall=1,1 OFFSET the offset for the start of the wall=0,0
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=uwall.bias,lwall.bias

Alternatively, if the input to this action is a vector as in the example shown below:

Click on the labels of the actions for more information on what each action computes

d1The DISTANCE action with label d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
d1
vector
the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=3,4 ATOMS3the pair of atom that we are calculating the distance between=5,6
uwallThe UPPER_WALLS action with label uwall calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_bias
scalar
the instantaneous value of the bias potential
uwall_force2
scalar
the instantaneous value of the squared force due to this bias potential: UPPER_WALLSDefines a wall for the value of one or more collective variables, This action is a shortcut. More details ARGthe arguments on which the bias is acting=d1 ATthe positions of the wall=1.0 KAPPAthe force constant for the wall=150.0 EXP the powers for the walls=2 EPS the values for s_i in the expression for a wall=1 OFFSET the offset for the start of the wall=0
# PLUMED interprets the command:
# uwall: UPPER_WALLS ARG=d1 AT=1.0 KAPPA=150.0 EXP=2 EPS=1 OFFSET=0
# as follows (Click the red comment above to revert to the short version of the input):
The UPPER_WALLS action with label uwall calculates the following quantities:
 Quantity   
 Description  
uwall.bias
the instantaneous value of the bias potential
uwall.force2
the instantaneous value of the squared force due to this bias potentialuwall_cv_d1The COMBINE action with label uwall_cv_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_cv_d1
vector
the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO ARGthe values input to this function=d1 PARAMETERS the parameters of the arguments in your function=1.0
uwall_scale_d1The CUSTOM action with label uwall_scale_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_scale_d1
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=(x+0)/1 ARGthe values input to this function=uwall_cv_d1
uwall_pow_d1The CUSTOM action with label uwall_pow_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_pow_d1
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=step(x)*x^2 ARGthe values input to this function=uwall_scale_d1
uwall_v_wall_d1The CUSTOM action with label uwall_v_wall_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_v_wall_d1
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=150.0*x ARGthe values input to this function=uwall_pow_d1
uwall_wall_d1The SUM action with label uwall_wall_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_wall_d1
scalar
the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=uwall_v_wall_d1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
uwall_force_d1The CUSTOM action with label uwall_force_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_force_d1
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=150.0*2*x/(y*1) ARGthe values input to this function=uwall_pow_d1,uwall_scale_d1
uwall_v_force2_d1The CUSTOM action with label uwall_v_force2_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_v_force2_d1
vector
the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO FUNCthe function you wish to evaluate=x*x ARGthe values input to this function=uwall_force_d1
uwall_force2_d1The SUM action with label uwall_force2_d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_force2_d1
scalar
the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=uwall_v_force2_d1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
uwall_biasThe COMBINE action with label uwall_bias calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_bias
scalar
a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO  ARGthe values input to this function=uwall_wall_d1
BIASVALUETakes the value of one variable and use it as a bias More details ARGthe labels of the scalar/vector arguments whose values will be used as a bias on the system=uwall_bias
The BIASVALUE action with label  calculates the following quantities:
 Quantity   
 Description  
.bias
the instantaneous value of the bias potential
._bias
one or multiple instances of this quantity can be referenced elsewhere in the input fileuwall_force2The COMBINE action with label uwall_force2 calculates the following quantities:
 Quantity   
 Type   
 Description  
uwall_force2
scalar
a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO  ARGthe values input to this function=uwall_force2_d1
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=uwall.bias

The bias that acts is given by the following expression:

$$\sum_i \sum_j {k_i}((x_{ij}-a_i+o_i)/s_i)^e_i$$

The sum over $i$ here is runs over the two arguments, while the sum over $j$ runs over the three components of the input vectors. Notice, that regardless of whether the input is a scalar, vector or matrix the number of $k_i$, $a_i$, $o_i$, $e_i$ and $s_i$ values must be equal to the number of arguments to the action.

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
ARG	scalar/vector	the arguments on which the bias is acting

Output components

This action calculates the values in the following table. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Description
bias	scalar	the instantaneous value of the bias potential
force2	scalar	the instantaneous value of the squared force due to this bias potential

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
ARG	input	none	the arguments on which the bias is acting
AT	compulsory	none	the positions of the wall
KAPPA	compulsory	none	the force constant for the wall
OFFSET	compulsory	0.0	the offset for the start of the wall
EXP	compulsory	2.0	the powers for the walls
EPS	compulsory	1.0	the values for s_i in the expression for a wall