Browsing Mathematics, Statistics & Physics by Author "Vuorinen, Matti"

Now showing items 1-9 of 9

    • Computation of conformal invariants 

      Mohamed M.S., Nasser; Vuorinen, Matti ( Elsevier , 2020 , Article)
      We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies to a wide variety ...

    • Condenser capacity and hyperbolic diameter 

      Mohamed M.S., Nasser; Rainio, Oona; Vuorinen, Matti ( Elsevier , 2021 , Article)
      Given a compact connected set E in the unit disk B2, we give a new upper bound for the conformal capacity of the condenser (B2,E) in terms of the hyperbolic diameter t of E. Moreover, for t>0, we construct a set of hyperbolic ...

    • Condenser capacity and hyperbolic perimeterImage 1 

      Mohamed M.S., Nasser; Rainio, Oona; Vuorinen, Matti ( Elsevier , 2021 , Article)
      We study the conformal capacity by using novel computational algorithms based on implementations of the fast multipole method, and analytic techniques. Especially, we apply domain functionals to study the capacities of ...

    • Conformal Invariants in Simply Connected Domains 

      Nasser, M.M.S.; Nasser, Mohamed M.S.; Vuorinen, Matti ( Springer Link , 2020 , Article)
      This paper studies the numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus ...

    • Isoperimetric properties of condenser capacity 

      Mohamed M.S., Nasser; Vuorinen, Matti ( Elsevier , 2021 , Article)
      For compact subsets E of the unit disk D we study the capacity of the condenser (D,E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic ...

    • Level sets of potential functions bisecting unbounded quadrilaterals 

      Nasser, Mohamed M.S.; Nasyrov, Semen; Vuorinen, Matti ( Springer Nature , 2022 , Article)
      We study the mixed Dirichlet–Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet / Neumann conditions at opposite pairs of ...

    • Numerical computation of Mityuk's function and radius for circular/radial slit domains 

      El Mostafa, Kalmoun; Nasser, Mohamed M.S.; Vuorinen, Matti ( Elsevier , 2020 , Article)
      We consider Mityuk's function and radius which have been proposed in [15] as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute ...

    • Numerical computation of the capacity of generalized condensers 

      Mohamed M.S., Nasser; Vuorinen, Matti ( Elsevier , 2020 , Article)
      We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates ...

    • Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals 

      Nasser, Mohamed; Rainio, Oona; Rasila, Antti; Vuorinen, Matti; Wallace, Terry; ... more authors ( Springer Nature , 2022 , Article)
      We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs, also called polycircular domains, and compute the moduli of quadrilaterals for these domains. ...