Stability Limits in Resonant Planetary Systems

The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the HD 82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant systems, the two stability boundaries are nearly coincident. However the Hill stability formula are not applicable to resonant systems, and our investigation shows how the two boundaries diverge in the presence of a mean-motion resonance, while confirming that the Hill and Lagrange boundaries are similar otherwise. In resonance the region of stability is larger than the domain defined by the analytic formula for Hill stability. We find that nearly all known resonant interactions currently lie in this extra stable region, i.e. where the orbits would be unstable according to the non-resonant Hill stability formula. This result bears on the dynamical packing of planetary systems, showing how quantifying planetary systems' dynamical interactions (such as proximity to the Hill-stability boundary) provides new constraints on planet formation models.Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ Letters. A version with full resolution figures is available at http://www.lpl.arizona.edu/~rory/research/xsp/resstab.pd

The Double Bind of Redevelopment: Camden During Receivership

This working paper finds that successful redevelopment efforts in Camden, New Jersey, under state receivership were able to build on groups' existing capacities and their past work in neighborhoods, were marked by more effective participatory dynamics and the limited use of eminent domain, and benefited from good relationships with the State of New Jersey and with private-sector partners. It concludes that attempts to build public capacity to revitalize cities may need to be complemented by efforts to build civic capacity, or the ability to solve problems in coordination with major partners

Empathy

After defining empathy, discussing its measurement, and offering an example of empathy in practice, we present the results of an updated meta-analysis of the relation between empathy and psychotherapy outcome. Results indicated that empathy is a moderately strong predictor of therapy outcome: mean weighted r = .31 ( p < .001; 95% confidence interval: .28 –.34), for 59 independent samples and 3599 clients. Although the empathy-outcome relation held equally for different theoretical orientations, there was considerable nonrandom variability. Client and observer perceptions of therapist empathy predicted outcomes better than therapist perceptions of empathic accuracy measures, and the relation was strongest for less experienced therapists. We conclude with practice recommendations, including endorsing the different forms that empathy may take in therapy

Quantum signal transmission through a single-qubit chain

A system of a two-level atom of an impurity (qubit) inserted into a periodic chain coupled to the continuum is studied with the use of the effective non-Hermitian Hamiltonian. Exact solutions are derived for the quasistationary eigenstates, their complex energies, and transport properties. Due to the presence of the qubit, two long-lived states corresponding to the ground and excited states of the qubit emerge outside the Bloch energy band. These states remain essentially localized at the qubit even in the limit of sufficiently strong coupling between the chain and the environment when the super-radiant states are formed. The transmission through the chain is studied as a function of the continuum coupling strength and the chain-qubit coupling; the perfect resonance transmission takes place through isolated resonances at weak and strong continuum coupling, while the transmission is lowered in the intermediate regime.Comment: In this version we added the case of large N and the case when the excitation energy of bare qubit is below the band boundary of the bare chain. The captions to some figures are modified. Some new references are adde

A cost-benefit analysis of pathways to work for new and repeat incapacity benefits claimants

This latest research forms part of a comprehensive independent evaluation of Pathways to Work. The report is based on a cost-benefit analysis conducted by a consortium of researchers from the Institute for Fiscal Studies, the University of Maryland, Baltimore County and the Policy Studies Institute. It examines whether the financial benefits from Pathways are larger or smaller than its costs and the generalisability of some of the quantitative findings. The estimates of costs and benefits relate to new and repeat incapacity benefits claimants in the seven original Jobcentre Plus districts. The overall findings provide a favourable impression of the financial benefits of the Pathways to Work for new and repeat incapacity benefits claimants, for the Exchequer and hence, for society as a whole

Why is CPT fundamental?

G. L\"uders and W. Pauli proved the $\mathcal{CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. R. Jost gave a more general proof based on ``axiomatic'' field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental--because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{CPT}$ transform of any relativistic field without calculating $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ separately and then multiplying them. The purpose of this pedagogical paper is to ``deaxiomatize'' the $\mathcal{CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.Comment: 17 pages, no figure

The Cocaine Cartel\u27s Best Kept Secret…The Black Market Peso Exchange; The Going Is Good, But For How Long, And At What price?

The date is July 2, 1991, piled upon rectangular tables are stacks of United States dollars

Topological Aspects of Spin and Statistics in Nonlinear Sigma Models

We study the purely topological restrictions on allowed spin and statistics of topological solitons in nonlinear sigma models. Taking as space the connected $d$-manifold $X$, and considering nonlinear sigma models with the connected manifold $M$ as target space, topological solitons are given by elements of $pi_d(M)$. Any topological soliton $\alpha \in \pi_d(M)$ determines a quotient \Stat_n(X,\alpha) of the group of framed braids on $X$, such that choices of allowed statistics for solitons of type $\alpha$ are given by unitary representations of \Stat_n(X,\alpha) when $n$ solitons are present. In particular, when $M = S^2$, as in the $O(3)$ nonlinear sigma model with Hopf term, and $\alpha \in \pi_2(S^2)$ is a generator, we compute that \Stat_n(\R^2,\alpha) = \Z, while \Stat_n(S^2,\alpha) = \Z_{2n}. It follows that phase $\exp(i\theta)$ for interchanging two solitons of type $\alpha$ on $S^2$ must satisfy the constraint $\theta = k\pi/n$, $k \in \Z$, when $n$ such solitons are present.Comment: 14 page

El Secreto Mas Guardado De Los Carteles De la Cocaina…El Intercanbio Del Peso En El Marcado Negro; El Negocio Es Bueno, Pero ἱPor Cuanto Tiempo, y A Que\u27 Precio?

La fecha es el 2 de julio de 1991, amontonadas sobre las mesas rectangulares se encuentran pilas de d6lares