In this paper, firstly, in $E_1^3$, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined fo...

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as " conformal " transports and investigated over (Ln, g)-spaces. They are more general than the Fermi-Walker transports. In an analogous way as in the case of Fermi-Walker transports a conformal covariant differential operator and its conformal der...

The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these frames can be explicitly constructed using either Killing or Killing-Yano tensors, the latter route chosen by Marck. For accelerated or geodesic circular orbits i...

In normal degenerate quark matter, the exchange of dynamically screened transverse gluons introduces infrared divergences in the quark self-energies that lead to the breakdown of the Fermi liquid description. If the core of neutron stars are composed of quark matter with a normal component, cooling by direct quark Urca processes may be modified by non-Fermi liquid corrections. We find that whil...

we derive error estimates in the appropriate norms, for the streamlinediffusion (sd) finite element methods for steady state, energy dependent,fermi equation in three space dimensions. these estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.high order sd method together with implicit integration are used. the formulationis strongly consistent...

The expansion of space, and other geometric properties of cosmological models, can be studied using geometrically defined notions of relative velocity. In this paper, we consider test particles undergoing radial motion relative to comoving (geodesic) observers in Robertson-Walker cosmologies, whose scale factors are increasing functions of cosmological time. Analytical and numerical comparisons...

The massless Dirac equation is studied in curved spacetime on the (2+1)-dimensional graphene sheet time-dependent geometries. Emergent pseudogauge fields are found both adiabatic regime and, for high-frequency periodic geometries, nonadiabatic a generic Friedmann-Lema\^itre-Robertson-Walker metric Fermi normal coordinates. former extends conventionally understood homogeneous field to include we...