The harmonic structure of generic Kerr orbits

Generic Kerr orbits exhibit intricate three-dimensional motion. We offer a classification scheme for these intricate orbits in terms of periodic orbits. The crucial insight is that for a given effective angular momentum $L$ and angle of inclination $\iota$, there exists a discrete set of orbits that are geometrically $n$-leaf clovers in a precessing {\it orbital plane}. When viewed in the full three dimensions, these orbits are periodic in $r-\theta$. Each $n$-leaf clover is associated with a rational number, $1+q_{r\theta}=\omega_\theta/\omega_r$, that measures the degree of perihelion precession in the precessing orbital plane. The rational number $q_{r\theta}$ varies monotonically with the orbital energy and with the orbital eccentricity. Since any bound orbit can be approximated as near one of these periodic $n$-leaf clovers, this special set offers a skeleton that illuminates the structure of all bound Kerr orbits, in or out of the equatorial plane.Comment: 14 pages, 8 figures. Submitted to Phys. Rev.

Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix

Under the dissipative effects of gravitational radiation, black hole binaries will transition from an inspiral to a plunge. The separatrix between bound and plunging orbits features prominently in the transition. For equatorial Kerr orbits, we show that the separatrix is a homoclinic orbit in one-to-one correspondence with an energetically-bound, unstable circular orbit. After providing a definition of homoclinic orbits, we exploit their correspondence with circular orbits and derive exact solutions for them. This paper focuses on homoclinic behavior in physical space, while in a companion paper we paint the complementary phase space portrait. The exact results for the Kerr separatrix could be useful for analytic or numerical studies of the transition from inspiral to plunge.Comment: 21 pages, some figure

Kurtuluş Savaşı'na karşı çıkan gazete

Taha Toros Arşivi, Dosya No: 228-Zeki Kuneral

Osmanlı şehzadelerinin hazin romanı

Taha Toros Arşivi, Dosya Adı: Son Halife Abdülmecit Efend

Atatürk:İnsanları seven bir insan

Taha Toros Arşivi, Dosya Adı: 1939-2000 Atatürk'ü Anma TörenleriKıyafetine büyük özen gösterirdiPolisler gelince, Ata'ya koştukİnsanlık sevgisi ile dopdoluyd

Influence of polymerisation conditions on the properties of polymer/clay nanocomposite hydrogels

Free-radical polymerisation of acrylamide derivatives in the presence of exfoliated clay platelets has recently emerged as a new technique for the synthesis of strong and tough nanocomposite hydrogels (NCHs) with a unique hybrid organic/inorganic network structure. The central intent of many research studies in the field of NCHs conducted so far was to change hydrogel properties with the introduction of various clays and variation of the clay content. Here, we demonstrate that the properties of NCHs significantly vary depending on initiating conditions used for hydrogel synthesis via in situ polymerisation in solutions of high monomer concentrations (above 1 mol L-1 ). A unique, complementary combination of real-time dynamic rheology and pulsed NMR/MRI has been used to study the influence of the composition of a redox initiating system on the gelation process and hydrogel properties. The molar ratio of the persulphate initiator to tertiary amine activator affects the polymerisation kinetics, morphology and mechanical properties of the hydrogels. We further show that activator-dominated systems tend to produce hydrogels with higher storage modulus and lower water intake. This trend is attributed to the increase in the cross-linking degree. From the analysis of the water state in NCH and hydrogels prepared with and without an organic cross-linker, it was concluded that clay platelets did not form covalent bonds with polymer molecules but contributed to the formation of a physical network. There is evidence of self-crosslinking of polymer chains during acrylamide polymerisation at high monomer concentration. The composition of the initiating system influences the number of formed self-crosslinks

Banks’ lending behaviour under repressed financial regulatory environment: in the context of Myanmar

In an ideal world, banking operations should ensure that there is a match between business strategy and loan assessment behaviour (Berger and Udell, 2004). However, in reality, banks are confined within a highly institutionalised environment which shapes their lending behaviour. Banks operate between two spectra in terms of regulatory environment, with policies based either on financial repression or liberalisation. Repressive policies are more common in the banking sector than capital markets. According to McKinnon (1973), financial repression is defined by various policies whereby the state influences credit allocation in channelling financial resources to priority areas identified by the government and micromanaging banks’ lending behaviour through interest-rate caps, collateral requirements and capital controls. Financial liberalisation, on the other hand, is regarded as an efficient means of fostering competition and inviting growth impulses from abroad (Bartolini and Drazen, 1997). After a series of decisions supporting financial liberalisation which took place from the 1970s to the 1990s, this type of policy has been intensively studied by scholars. However, there is still no consensus on whether it has positive or negative impacts