Geodesic orbits about an axisymmetric mass distribution

The General Theory of Relativity (GRT) gives rise to many interesting questions, one of which is a question about how test particles orbit various relativistic mass configurations. A test particle is defined as an electrically neutral particle small enough that its self gravitating energy, as calculated using standard Newtonian theory, can be neglected when compared with the particle\u27s rest mass, ie. M/R \u3c\u3c 1. (Here M is the mass of the particle in meters, and R is the radius of the particle again in meters. The mass of the sun in these units is 1.47 km.) For example, the earth, which can be considered a test particle for the sun, travels about the sun in an elliptic orbit. What would happen if the sun suddenly became a black-hole? How would the earth\u27s orbit be affected? It is the purpose of this paper to answer these questions not only for the case of the spherical black-hole (which has been extensively studied), but also for the case of an axisymmetric mass distribution idealized by a long thin rod-like mass (which will henceforth be referred to as a line mass). The classical case and relativistic case concerning orbits about the line mass will be discussed, along with some interesting features of the relativistic line mass orbits. Some background information concerning GRT will be needed before the problem of line mass is approached

Missing data in randomized controlled trials testing palliative interventions pose a significant risk of bias and loss of power: a systematic review and meta-analyses

Objectives To assess the risk posed by missing data (MD) to the power and validity of trials evaluating palliative interventions. Study Design and Setting A systematic review of MD in published randomized controlled trials (RCTs) of palliative interventions in participants with life-limiting illnesses was conducted, and random-effects meta-analyses and metaregression were performed. CENTRAL, MEDLINE, and EMBASE (2009-2014) were searched with no language restrictions. Results One hundred and eight RCTs representing 15,560 patients were included. The weighted estimate for MD at the primary endpoint was 23.1% (95% confidence interval [CI] 19.3, 27.4). Larger MD proportions were associated with increasing numbers of questions/tests requested (odds ratio [OR] , 1.19; 95% CI 1.05, 1.35) and with longer study duration (OR, 1.09; 95% CI 1.02, 1.17). Meta-analysis found evidence of differential rates of MD between trial arms, which varied in direction (OR, 1.04; 95% CI 0.90, 1.20; I 2 35.9, P = 0.001). Despite randomization, MD in the intervention arms (vs. control) were more likely to be attributed to disease progression unrelated to the intervention (OR, 1.31; 95% CI 1.02, 1.69). This was not the case for MD due to death (OR, 0.92; 95% CI 0.78, 1.08). Conclusion The overall proportion and differential rates and reasons for MD reduce the power and potentially introduce bias to palliative care trials

Electrostatic interactions mediated by polarizable counterions: weak and strong coupling limits

We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak- and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.Comment: 25 pages, 7 figure

Langevin Equation for the Density of a System of Interacting Langevin Processes

We present a simple derivation of the stochastic equation obeyed by the density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological equations usually used to describe the dynamics of non conserved (Model A) and conserved (Model B) particle systems. The major feature is that the spatial white noise for this system appears not additively but multiplicatively. This simply expresses the fact that the density cannot fluctuate in regions devoid of particles. The steady state for the density function may however still be recovered formally as a functional integral over the coursed grained free energy of the system as in Models A and B.Comment: 6 pages, latex, no figure

Direct Detection of Products from the Pyrolysis of 2-Phenethyl Phenyl Ether

The pyrolysis of 2-phenethyl phenyl ether (PPE, C_6H_5C_2H_4OC_6H_5) in a hyperthermal nozzle (300-1350 °C) was studied to determine the importance of concerted and homolytic unimolecular decomposition pathways. Short residence times (<100 μs) and low concentrations in this reactor allowed the direct detection of the initial reaction products from thermolysis. Reactants, radicals, and most products were detected with photoionization (10.5 eV) time-of-flight mass spectrometry (PIMS). Detection of phenoxy radical, cyclopentadienyl radical, benzyl radical, and benzene suggest the formation of product by the homolytic scission of the C_6H_5C_2H_4-OC_6H_5 and C_6H_5CH_2-CH_2OC_6H_5 bonds. The detection of phenol and styrene suggests decomposition by a concerted reaction mechanism. Phenyl ethyl ether (PEE, C_6H_5OC_2H_5) pyrolysis was also studied using PIMS and using cryogenic matrix-isolated infrared spectroscopy (matrix-IR). The results for PEE also indicate the presence of both homolytic bond breaking and concerted decomposition reactions. Quantum mechanical calculations using CBS-QB3 were conducted, and the results were used with transition state theory (TST) to estimate the rate constants for the different reaction pathways. The results are consistent with the experimental measurements and suggest that the concerted retro-ene and Maccoll reactions are dominant at low temperatures (below 1000 °C), whereas the contribution of the C_6H_5C_2H_4-OC_6H_5 homolytic bond scission reaction increases at higher temperatures (above 1000 °C)

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Bifurcated polarization rotation in bismuth-based piezoelectrics

ABO3 perovskite-type solid solutions display a large variety of structural and physical properties, which can be tuned by chemical composition or external parameters such as temperature, pressure, strain, electric, or magnetic fields. Some solid solutions show remarkably enhanced physical properties including colossal magnetoresistance or giant piezoelectricity. It has been recognized that structural distortions, competing on the local level, are key to understanding and tuning these remarkable properties, yet, it remains a challenge to experimentally observe such local structural details. Here, from neutron pair-distribution analysis, a temperature-dependent 3D atomic-level model of the lead-free piezoelectric perovskite Na0.5Bi0.5TiO3 (NBT) is reported. The statistical analysis of this model shows how local distortions compete, how this competition develops with temperature, and, in particular, how different polar displacements of Bi3+ cations coexist as a bifurcated polarization, highlighting the interest of Bi-based materials in the search for new lead-free piezoelectrics

Non-monotoic fluctuation-induced interactions between dielectric slabs carrying charge disorder

We investigate the effect of monopolar charge disorder on the classical fluctuation-induced interactions between randomly charged net-neutral dielectric slabs and discuss various generalizations of recent results (A. Naji et al., Phys. Rev. Lett. 104, 060601 (2010)) to highly inhomogeneous dielectric systems with and without statistical disorder correlations. We shall focus on the specific case of two generally dissimilar plane-parallel slabs, which interact across vacuum or an arbitrary intervening dielectric medium. Monopolar charge disorder is considered to be present on the bounding surfaces and/or in the bulk of the slabs, may be in general quenched or annealed and may possess a finite lateral correlation length reflecting possible `patchiness' of the random charge distribution. In the case of quenched disorder, the bulk disorder is shown to give rise to an additive long-range contribution to the total force, which decays as the inverse distance between the slabs and may be attractive or repulsive depending on the dielectric constants of the slabs. We show that in the case of two dissimilar slabs the net effect due to the interplay between the disorder-induced and the pure van der Waals interactions can lead to a variety of unusual non-monotonic interaction profiles between the dielectric slabs. In particular, when the intervening medium has a larger dielectric constant than the two slabs, we find that the net interaction can become repulsive and exhibit a potential barrier, while the underlying van der Waals force is attractive. On the contrary, when the intervening medium has a dielectric constant in between that of the two slabs, the net interaction can become attractive and exhibit a free energy minimum, while the pure van der Waals force is repulsive. Therefore, the charge disorder, if present, can drastically alter the effective interaction between net-neutral objects.Comment: 13 pages, 8 figure