Filtreler

Filtreleri Sıfırla

Ayarlar

Bölüm: Işık University, Faculty of Arts and Sciences, Department of Mathematics × Konu: Equations ×

Arama Sonuçları

Listeleniyor 1 - 5 / 5
  • Küçük Resim
    Yayın
    On complex solutions of the eikonal equation
    (IEEE, 2007) Hasanoğlu, Elman
    In this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.
  • Küçük Resim
    Yayın
    Particle dynamics in the KdV approximation
    (Elsevier Science BV, 2012-12) Borluk, Handan; Kalisch, Henrik
    The KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed numerically. The solutions treated here comprise the solitary wave, periodic traveling waves, and the two-soliton solutions. For solitary waves and periodic traveling waves, approximate particle paths are found in closed form.
  • Küçük Resim
    Yayın
    Complex and real rays in three dimensional Minkowski space
    (IEEE, 2002) Hasanoğlu, Elman
    A new approach to the theory of complex rays is proposed. It is shown that the Minkowski space is more appropriate for describing these rays than the usual, Euclidian spaces. Some illustrative examples are represented.
  • Küçük Resim
    Yayın
    Matched pair analysis of the Vlasov plasma
    (American Institute of Mathematical Sciences-AIMS, 2021-06) Esen, Oğul; Sütlü, Serkan
    We present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order >= 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.
  • Küçük Resim
    Yayın
    Beam tracing theory in Minkowski space
    (IEEE, 2011) Hasanoğlu, Elman
    This paper provides a novel approach to beam theory in homogeneous lossless mediun. The main idea is to interpret the classic eikonal equation in three dimensional Minkowski space.