We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to ...

A boundary layer’s appearance in a diverging permeable channel for non-Newtonian hyperbolic tangent fluid with heat transfer the availability of source and suction or injection is investigated. By controlling backflow, nonlinearly associated ODEs are derived from flow-regulating PDEs, restrictions under which formation layer emerges It obtained that mass an expression Hartmann number, porosity ...

A new figure correction method has been applied in order to fabricate an elliptical mirror to realize a one-dimensionally diverging X-ray beam having high image quality. Mutual relations between figure errors and intensity uniformities of diverging X-ray beams have also been investigated using a wave-optical simulator and indicate that figure errors in relatively short spatial wavelength ranges...

The diverging and converging field components of the source-free focus wave modes are studied within the framework of both the Whittaker and Weyl plane wave expansions. It is shown that, in the Weyl picture, the evanescent fields associated with the diverging and converging components of the focus wave mode solution cancel each other identically. The source-free focus wave modes are, hence, com...