Patent ID: 11885568
Assignee: LAWRENCE LIVERMORE NATIONAL SECURITY, LLC
Field: Chemical engineering (Chemistry)
Classification: CPC B  F  Y | IPC B  F

Claim 12:
13. The apparatus of claim 12, wherein each of the cells forms a unit cell, and wherein a size gradient of each of the unit cells is controlled in accordance with a formula:

Lmodified=L+(1−Hε(φ))Lf 

where L is a length of the unit cell, and f a shrinkage or expansion factor of the unit cell;
where Hε(φ) is a smoothed Heaviside function which determines a variation of a graded zone:, H
      ɛ
    
    ⁡
    
      (
      ϕ
      )
    
  
  =
  
    {
    
      
        
          
            1
            ,
          
        
        
          
            ϕ
            <
            
              -
              ɛ
            
          
        
      
      
        
          
            
              [
              
                1
                +
                
                  ϕ
                  ɛ
                
                +
                
                  
                    1
                    π
                  
                  ⁢
                  
                    sin
                    ⁡
                    
                      (
                      
                        
                          π
                          ⁢
                          ϕ
                        
                        ɛ
                      
                      )
                    
                  
                
              
              ]
            
            ,
          
        
        
          
            
              
              ϕ
              
            
            ≤
            ɛ
          
        
      
      
        
          
            0
            ,
          
        
        
          
            ϕ
            >
            ɛ, and where φ(x, y, z) is a level set function to determine where a modification in a size gradient takes place along the apparatus.