In this paper, we explore the interior dynamics of neutral and charged black holes in f(R) gravity. We transform f(R) gravity from the Jordan frame into the Einstein frame and simulate scalar collapses in flat, Schwarzschild, and Reissner-Nordström geometries. In simulating scalar collapses in Schwarzschild and Reissner-Nordström geometries, Kruskal and Kruskal-like coordinates are used, respec...

A system of difference equations of the first order with meromorphic coefficients (not necessary periodic ones) subject to certain conditions of symmetry is analysed. These conditions arise in model problems of diffraction theory. A method for the constructive solution of the system of difference equations is proposed. It consists of three steps. First, it requires factorization of a certain fu...

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies ν of the order or higher than the frequency associated with the Kondo effect k(B)T (K)/h, with TK the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for hν ≈ k(B)T(K)...

We survey rigorous, formal, and numerical results on the formation of point-like singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blow-up point, such that self-similar behaviour is mapped to the fixed point of a dynamical system. We point out that analysing the dynamics close to the fixed point is...

We survey rigorous, formal and numerical results on the formation of pointlike singularities (or blow-up) for a wide range of evolution equations. We use a similarity transformation of the original equation with respect to the blowup point, such that self-similar behaviour is mapped to the fixed point of a dynamical system. We point out that analysing the dynamics close to the fixed point is a ...

Dynamics of an intense short laser pulse with a phase singularity, propagating in an underdense cold plasma, is investigated. Such a pulse can propagate as a vortex soliton in a self-created channel. It is shown that vortices with the topological charge m=1,2 (and a corresponding angular momentum) are unstable against symmetry-breaking perturbations; the breakup of the original vortex leads to ...

Rotating spiral waves without phase singularity are found to arise in a certain class of three-component reaction-diffusion systems of biological relevance. It is argued that this phenomenon is universal when some chemical components involved are diffusion-free. Some more detailed mathematical and numerical analyses are carried out on a complex GinzburgLandau equation with non-local coupling to...

Reverse bubbling refers to singularities which develop in geometric flows as one takes a reverse limit t ↓ T rather than the traditional t ↑ T . Flows with this type of singularity may have different or better properties, and can provide alternative ways of flowing past singularities. We survey the original reverse bubbling theory for the harmonic map flow, including recent developments, and ot...

The cosmological compactification of D = 10 , N = 1 supergravity– super–Yang–Mills theory obtained from superstring theory is studied. The constraint of unbroken N = 1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontr...

The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, supersymmetric dilatonic waves and one possible resolution of its singularity in terms of nullbranes are also discussed. PACS numbers: 11.15.kc, 1...