Effect of gravitational radiation reaction on nonequatorial orbits around a Kerr black hole

The effect of gravitational radiation reaction on orbits around a spinning black hole is analyzed. Such orbits possess three constants of motion: iota, e, and a, which correspond, in the Newtonian limit of the orbit being an ellipse, to the inclination angle of the orbital plane to the hole's equatorial plane, the eccentricity, and the semimajor axis length, respectively. First, it Is argued that circular orbits (e = 0) remain circular under gravitational radiation reaction. Second, for elliptical orbits (removing the restriction of e = 0), the evolution of iota, e, and a is computed to leading order in S (the magnitude of the spin angular momentum of the hole) and in M/a, where M is the mass of the black hole. As a decreases, iota increases and e decreases

Effect of gravitational radiation reaction on circular orbits around a spinning black hole

The effect of gravitational radiation reaction on circular orbits around a spinning (Kerr) black hole is computed to leading order in $S$ (the magnitude of the spin angular momentum of the hole) and in the strength of gravity $M/r$ (where $M$ is the mass of the black hole, $r$ is the orbital radius, and $G=c=1$). The radiation reaction makes the orbit shrink but leaves it circular, and drives the orbital plane very slowly toward antialignment with the spin of the hole: $\tan (\iota /2) = \tan (\iota_0 /2) [1+(61/72)(S/M^2) (M/r)^{3/2}]$, where $\iota$ is the angle between the normal to the orbital plane and the spin direction, and $\iota_0$ is the initial value of $\iota$, when $r$ is very large.Comment: 12 page

Who Cares How Congress Really Works?

Legislative intent is a fiction. Courts and scholars accept this, by and large. As this Article shows, however, both are confused as to why legislative intent is a fiction and as to what this fiction entails. This Article first argues that the standard explanation—that Congress is a “they,” not an “it”—rests on an unduly simple conception of shared agency. Drawing from contemporary scholarship in the philosophy of action, it contends that Congress has no collective intention, not because of difficulties in aggregating the intentions of individual members, but rather because Congress lacks the sort of delegatory structure that one finds in, for example, a corporation. Second, this Article argues that—contrary to a recent, influential wave of scholarship—the fictional nature of legislative intent leaves interpreters of legislation with little reason to care about the fine details of legislative process. It is a platitude that legislative text must be interpreted in “context.” Context, however, consists of information salient to author and audience alike. This basic insight from the philosophy of language necessitates what this Article calls the “conversation” model of interpretation. Legislation is written by legislators for those tasked with administering the law—for example, courts and agencies—and those on whom the law operates—for example, citizens. Almost any interpreter thus occupies the position of conversational participant, reading legislative text in a context consisting of information salient both to members of Congress and to citizens (as well as agencies, courts, etc.). The conversation model displaces what this Article calls the “eavesdropping” model of interpretation—the prevailing paradigm among both courts and scholars. When asking what sources of information an interpreter should consider, courts and scholars have reliably privileged the epistemic position of members of Congress. The result is that legislation is erroneously treated as having been written by legislators exclusively for other legislators. This tendency is plainest in recent scholarship urging greater attention to legislative process—the nuances of which are of high salience to legislators but plainly not to citizens

The Effect of Slow Two‐Electron Transfers and Disproportionation on Cyclic Voltammograms

The EE mechanism (two‐electron transfer) for cyclic voltammetry was investigated in considerable detail along with the effect of disproportionation. The theory was developed for either the first or second electron transfer being slow while the other one was reversible. It was possible to develop generalized working curves for the height and shape of the wave regardless of the difference in Eo\u27s and the values of α and Ks. This theory was then applied to the analysis of the reduction of benzil in the presence of alkaline earth ions in dimethylformamide

Diffusion Approximations for Demographic Inference: DaDi

Models of demographic history (population sizes, migration rates, and divergence times) inferred from genetic data complement archeology and serve as null models in genome scans for selection. Most current inference methods are computationally limited to considering simple models or non-recombining data. We introduce a method based on a diffusion approximation to the joint frequency spectrum of genetic variation between populations. Our implementation, DaDi, can model up to three interacting populations and scales well to genome-wide data. We have applied DaDi to human data from Africa, Europe, and East Asia, building the most complex statistically well-characterized model of human migration out of Africa to date

Spectroscopic Evidence of Nanodomains in THF/RTIL Mixtures: Spectroelectrochemical and Voltammetric Study of Nickel Porphyrins

The presence and effect of RTIL nanodomains in molecular solvent/RTIL mixture were investigated by studying the spectroelectrochemistry and voltammetry of nickel octaethylporphyrin (Ni(OEP)) and nickel octaethylporphinone (Ni(OEPone)). Two oxidation and 2–3 reduction redox couples were observed, and the UV–visible spectra of all stable products in THF and RTIL mixtures were obtained. The E° values for the reduction couples that were studied were linearly correlated with the Gutmann acceptor number, as well as the difference in the E° values between the first two waves (ΔE12° = |E1° – E2°|). The ΔE12° for the reduction was much more sensitive to the %RTIL in the mixture than the oxidation, indicating a strong interaction between the RTIL and the anion or dianion. The shifts in the E° values were significantly different between Ni(OEP) and Ni(OEPone). For Ni(OEP), the E1° values were less sensitive to the %RTIL than were observed for Ni(OEPone). Variations in the diffusion coefficients of Ni(OEP) and Ni(OEPone) as a function of %RTIL were also investigated, and the results were interpreted in terms of RTIL nanodomains. To observe the effect of solvation on the metalloporphyrin, Ni(OEPone) was chosen because it contains a carbonyl group that can be easily observed in infrared spectroelectrochemistry. It was found that the νCO band was very sensitive to the solvent environment, and two carbonyl bands were observed for Ni(OEPone)− in mixed THF/RTIL solutions. The higher energy band was attributed to the reduced product in THF, and the lower energy band attributed to the reduced product in the RTIL nanophase. The second band could be observed with as little as 5% of the RTIL. No partitioning of Ni(OEPone)+ into the RTIL nanodomain was observed. DFT calculations were carried out to characterize the product of the first reduction. These results provide strong direct evidence of the presence of nanodomains in molecular solvent/RTIL mixtures

Electrochemistry and Spectroelectrochemistry of 1,4-Dinitrobenzene in Acetonitrile and Room-Temperature Ionic Liquids: Ion-Pairing Effects in Mixed Solvents

Room-temperature ionic liquids (RTILs) have been shown to have a significant effect on the redox potentials of compounds such as 1,4-dinitrobenzene (DNB), which can be reduced in two one-electron steps. The most noticeable effect is that the two one-electron waves in acetonitrile collapsed to a single two-electron wave in a RTIL such as butylmethyl imidazolium-BF4 (BMImBF4). In order to probe this effect over a wider range of mixed-molecular-solvent/RTIL solutions, the reduction process was studied using UV–vis spectroelectrochemistry. With the use of spectroelectrochemistry, it was possible to calculate readily the difference in E°’s between the first and second electron transfer (ΔE12° = E1° – E2°) even when the two one-electron waves collapsed into a single two-electron wave. The spectra of the radical anion and dianion in BMImPF6 were obtained using evolving factor analysis (EFA). Using these spectra, the concentrations of DNB, DNB–•, and DNB2– were calculated, and from these concentrations, the ΔE12° values were calculated. Significant differences were observed when the bis(trifluoromethylsulfonyl)imide (NTf2) anion replaced the PF6– anion, leading to an irreversible reduction of DNB in BMImNTf2. The results were consistent with the protonation of DNB2–, most likely by an ion pair between DNB2– and BMIm+, which has been proposed by Minami and Fry. The differences in reactivity between the PF6– and NTf2– ionic liquids were interpreted in terms of the tight versus loose ion pairing in RTILs. The results indicated that nanostructural domains of RTILs were present in a mixed-solvent system

Electrochemistry and spectroelectrochemistry of iron porphyrins in the presence of nitrite

The reaction of nitrite with ferric and ferrous porphyrins was examined using visible, infrared and NMR spectroscopy. Solutions of either ferric or ferrous porphyrin were stable in the presence of nitrite, with only complexation reactions being observed. Under voltammetric conditions, though, a rapid reaction between nitrite and iron porphyrins was observed to form the nitrosyl complex, Fe(p)(NO), where Pporphyrins. The products of the reduction of ferric porphyrins in the presence of nitrite were confirmed by visible spectroelectrochemistry to be Fe(P)(NO) and [Fe(P)]2O. Visible, NMR and infrared spectroscopy were used to rule out the formation of Fe(P)(NO) by the iron-catalyzed disproportionation of nitrite. A reaction between iron porphyrins and nitrite only occurred by the presence of both oxidation states (ferric:ferrous). The kinetics of the reaction were monitored by visible spectroscopy, and the reaction was found to be first-order with respect to Fe(OEP)(Cl) and Fe(OEP). The products were the same as those observed in the spectroelectrochemical experiment. The rate was not strongly dependent upon the concentration of nitrite, indicating that the coordinated, not the free nitrite, was the reaction species. The kinetics observed were consistent with a mixed oxidation state nitrite-bridged intermediate, which carried out the oxygen transfer reaction from nitrite to the iron porphyrin. The effect of nitrite coordination on the reaction rate was examined. © 2001 Elsevier Science B.V. All rights reserved