'The world is full of big bad wolves': investigating the experimental therapeutic spaces of R.D. Laing and Aaron Esterson

In conjunction with the recent critical assessments of the life and work of R.D. Laing, this paper seeks to demonstrate what is revealed when Laing’s work on families and created spaces of mental health care are examined through a geographical lens. The paper begins with an exploration of Laing’s time at the Tavistock Clinic in London during the 1960s, and of the co-authored text with Aaron Esterson entitled, Sanity, Madness and the Family (1964). The study then seeks to demonstrate the importance Laing and his colleague placed on the time-space situatedness of patients and their worlds. Finally, an account is provided of Laing’s and Esterson’s spatial thinking in relation to their creation of both real and imagined spaces of therapeutic care

Chimera states in networks of phase oscillators: the case of two small populations

Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in the continuum limit, chimeras may also occur in systems with finite (and small) numbers of oscillators. Focusing on networks of $2N$ phase oscillators that are organized in two groups, we find that chimera states, corresponding to attracting periodic orbits, appear with as few as two oscillators per group and demonstrate that for $N>2$ the bifurcations that create them are analogous to those observed in the continuum limit. These findings suggest that chimeras, which bear striking similarities to dynamical patterns in nature, are observable and robust in small networks that are relevant to a variety of real-world systems.Comment: 13 pages, 16 figure

Nonlinear stability of relativistic sheared planar jets

The linear and non-linear stability of sheared, relativistic planar jets is studied by means of linear stability analysis and numerical hydrodynamical simulations. Our results extend the previous Kelvin-Hemlholtz stability studies for relativistic, planar jets in the vortex sheet approximation performed by Perucho et al. (2004a,b) by including a shear layer between the jet and the external medium and more general perturbations. The models considered span a wide range of Lorentz factors ($2.5-20$) and internal energies ($0.08 c^2-60 c^2$) and are classified into three classes according to the main characteristics of their long-term, non-linear evolution. We observe a clear separation of these three groups in a relativistic Mach-number Lorentz-factor plane. Jets with a low Lorentz factor and small relativistic Mach number are disrupted after saturation. Those with a large Lorentz factor and large relativistic Mach number are the stablest, due to the appearance of short wavelength resonant modes which generate local mixing and heating in the shear layer around a fast, unmixed core, giving a plausible solution for the problem of the long-term stability of relativistic jets. A third group is present between them, including jets with intermediate values of Lorentz factor and relativistic Mach number, which are disrupted by a slow process of mixing favored by an efficient and continuous conversion of kinetic into internal energy. In the long term, all the models develop a distinct transversal structure (shear/transition layers) as a consequence of KH perturbation growth, depending on the class they belong to. The properties of these shear layers are analyzed in connection with the parameters of the original jet models.Comment: accepted for publication in A&A (in press). High resolution plots, figures and Appendices of the paper will be found in the online version of the paper in A&A, and on request to [email protected]

The impact of instrument choice on investment in abatement technologies: a case study of tax versus trade incentives for CCS and Biomass for electricity

There has been a wide discussion on the different properties between carbon taxes, cap-and-trade schemes and hybrid instruments such as cap-and-trade schemes with price floors and ceilings. There has been less discussion on the incentives to investment that each of these instruments may provide. We build a three-period model to investigate the incentives offered to a large firm with diversified abatement options from such instruments when facing a choice between investing in lowcarbon technologies with potential learning benefits. We parameterise our model for a system similar to the EUETS and for two sample technologies, biomass for electricity and coal with carbon capture and storage. For both technologies we find that cap-and-trade schemes generate greater mean returns to such an investment than taxes, but with a wider distribution. We find that introducing price floors increase such mean returns while reducing the distribution, while ceilings further reduce the distribution, but also the mean and thus the overall incentives they offer will depend on the risk preference of the firm and scale of investment in relation to overall compliance costs

Experimental Quantum Process Discrimination

Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of non-orthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination (QPD) of non-orthogonal processes using properties of entanglement, additional known unitaries, or higher dimensional systems. Single qubit measurement and unitary processes and multipartite unitaries (where the unitary acts non-separably across two distant locations) acting on photons are discriminated with a confidence of $\geq97$ in all cases.Comment: 4 pages, 3 figures, comments welcome. Revised version includes multi-partite QP

An Attempt to Probe the Radio Jet Collimation Regions in NGC 4278, NGC 4374 (M84), and NGC 6166

NRAO Very Long Baseline Array (VLBA) observations of NGC 4278, NGC 4374 (M84), NGC 6166, and M87 (NGC 4486) have been made at 43 GHz in an effort to image the jet collimation region. This is the first attempt to image the first three sources at 43 GHz using Very Long Baseline Interferometry (VLBI) techniques. These three sources were chosen because their estimated black hole mass and distance implied a Schwarzschild radius with large angular size, giving hope that the jet collimation regions could be studied. Phase referencing was utilize for the three sources because of their expected low flux densities. M87 was chosen as the calibrator for NGC 4374 because it satisfied the phase referencing requirements: nearby to the source and sufficiently strong. Having observed M87 for a long integration time, we have detected its sub-parsec jet, allowing us to confirm previous high resolution observations made by Junor, Biretta & Livio, who have indicated that a wide opening angle was seen near the base of the jet. Phase referencing successfully improved our image sensitivity, yielding detections and providing accurate positions for NGC 4278, NGC 4374 and NGC 6166. These sources are point dominated, but show suggestions of extended structure in the direction of the large-scale jets. However, higher sensitivity will be required to study their sub-parsec jet structure

Multifrequency VLA observations of the FR I radio galaxy 3C 31: morphology, spectrum and magnetic field

We present high-quality VLA images of the FR I radio galaxy 3C 31 in the frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40 arcsec. Our new images reveal complex, well resolved filamentary substructure in the radio jets and tails. We also use these images to explore the spectral structure of 3C 31 on large and small scales. We infer the apparent magnetic field structure by correcting for Faraday rotation. Some of the intensity substructure in the jets is clearly related to structure in their apparent magnetic field: there are arcs of emission where the degree of linear polarization increases, with the apparent magnetic field parallel to the ridges of the arcs. The spectral indices are significantly steeper (0.62) within 7 arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra of the jet edges are also slightly flatter than the average for their surroundings. At larger distances, the jets are clearly delimited from surrounding larger-scale emission both by their flatter radio spectra and by sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of 3C 31's jets is very close to that found in other FR I galaxies where their jets first brighten in the radio and where X-ray synchrotron emission is most prominent. Farther from the nucleus, where the spectra flatten, X-ray emission is fainter relative to the radio. The brightest X-ray emission from FR I jets is therefore not associated with the flattest radio spectra, but with a particle-acceleration process whose characteristic energy index is 2.24. The spectral flattening with distance from the nucleus occurs where our relativistic jet models require deceleration, and the flatter-spectra at the jet edges may be associated with transverse velocity shear. (Slightly abridged)Comment: 17 pages, 13 figures, accepted for publication in MNRA

On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem

Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spatial dimensions. The symmetric structure at lowest order has a point group isomorphic with the S_N group, the symmetric group of N particles, and the resulting perturbation expansion of the Hamiltonian is order-by-order invariant under the permutations of the S_N group. This invariance under S_N imposes severe symmetry requirements on the tensor blocks needed at each order in the perturbation series. We show here that these blocks can be decomposed into a basis of binary tensors invariant under S_N. This basis is small (25 terms at first order in the wave function), independent of N, and is derived using graphical techniques. This checks the N^6 scaling of these terms at first order by effectively separating the N scaling problem away from the rest of the physics. The transformation of each binary tensor to the final normal coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N for arbitrary N. This has been accomplished using the group theory of the symmetric group. This achievement results in an analytic solution for the wave function, exact through first order, that scales as N^0, effectively circumventing intensive numerical work. This solution can be systematically improved with further analytic work by going to yet higher orders in the perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and is under revie

Structure of the magnetoionic medium around the FR Class I radio galaxy 3C 449

The goal of this work is to constrain the strength and structure of the magnetic field associated with the environment of the radio source 3C 449, using observations of Faraday rotation, which we model with a structure function technique and by comparison with numerical simulations. We assume that the magnetic field is a Gaussian, isotropic random variable and that it is embedded in the hot intra-group plasma surrounding the radio source. For this purpose, we present detailed rotation measure images for the polarized radio source 3C 449, previously observed with the Very Large Array at seven frequencies between 1.365 and 8.385 GHz. We quantify the statistics of the magnetic-field fluctuations by deriving rotation measure structure functions, which we fit using models derived from theoretical power spectra. We quantify the errors due to sampling by making multiple two-dimensional realizations of the best-fitting power spectrum.We also use depolarization measurements to estimate the minimum scale of the field variations. We then make three-dimensional models with a gas density distribution derived from X-ray observations and a random magnetic field with this power spectrum. Under these assumptions we find that both rotation measure and depolarization data are consistent with a broken power-law magnetic-field power spectrum, with a break at about 11 kpc and slopes of 2.98 and 2.07 at smaller and larger scales respectively. The maximum and minimum scales of the fluctuations are around 65 and 0.2 kpc, respectively. The average magnetic field strength at the cluster centre is 3.5 +/-1.2 micro-G, decreasing linearly with the gas density within about 16 kpc of the nucleus.Comment: 19 pages; 14 figures; accepted for publication on A&A. For a high quality version use ftp://ftp.eso.org/pub/general/guidetti