An integral equation method for the inverse conductivity problem

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity. We have used a priori information to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind for the Laplacian of the potential, and then by solving a first order partial differential equation for the regularized conductivity itself. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.Comment: 15 pages, 8 figure

Nature of the spin dynamics and 1/3 magnetization plateau in azurite

We present a specific heat and inelastic neutron scattering study in magnetic fields up into the 1/3 magnetization plateau phase of the diamond chain compound azurite Cu$_3$(CO$_3$)$_2$(OH)$_2$. We establish that the magnetization plateau is a dimer-monomer state, {\it i.e.}, consisting of a chain of $S = 1/2$ monomers, which are separated by $S = 0$ dimers on the diamond chain backbone. The effective spin couplings $J_{mono}/k_B = 10.1(2)$ K and $J_{dimer}/k_B = 1.8(1)$ K are derived from the monomer and dimer dispersions. They are associated to microscopic couplings $J_1/k_B = 1(2)$ K, $J_2/k_B = 55(5)$ K and a ferromagnetic $J_3/k_B = -20(5)$ K, possibly as result of $d_{z^2}$ orbitals in the Cu-O bonds providing the superexchange pathways.Comment: 5 pages, 4 figure

Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)$_2$P$_2$O$_7$, the effects of two energy scales of the weakly dimerized antiferromagnetic $S$ = 1/2 Heisenberg chain are explored. The low energy scale, given by the spin gap $\Delta$, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing T-DMRG calculations, shows that this feature originates from changes in the magnetic entropy with respect to $\Delta$, $\partial S^{m}/ \partial \Delta$. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in $\Delta$.Comment: 4 pages, 4 figures now identical with finally published versio

Magnetoelastic and structural properties of azurite Cu3(CO3)2(OH)2 from neutron scattering and muon spin rotation

Azurite, Cu3(CO3)2(OH)2, has been considered an ideal example of a one-dimensional (1D) diamond chain antiferromagnet. Early studies of this material imply the presence of an ordered antiferromagnetic phase below $T_N \sim 1.9$ K while magnetization measurements have revealed a 1/3 magnetization plateau. Until now, no corroborating neutron scattering results have been published to confirm the ordered magnetic moment structure. We present recent neutron diffraction results which reveal the presence of commensurate magnetic order in azurite which coexists with significant magnetoelastic strain. The latter of these effects may indicate the presence of spin frustration in zero applied magnetic field. Muon spin rotation, $\mu$SR, reveals an onset of short-range order below 3K and confirms long-range order below $T_N$.Comment: 5 pages, 4 figures, PHYSICAL REVIEW B 81, 140406(R) (2010

Critical Phenomena at the Antiferromagnetic Phase Transition of Azurite

We report on high-resolution acoustic, specific-heat and thermal expansion measurements in the vicinity of the antiferromagnetic phase transition at T_N = 1.88 K on a high-quality single crystal of the natural mineral azurite. A detailed investigation of the critical contribution to the various quantities at T_N is presented. The set of critical exponents and amplitude ratios of the singular contributions above and below the transition indicate that the system can be reasonably well described by a three-dimensional Heisenberg antiferromagnet.Comment: 9 pages, 3 figures, proceedings of ICM 2012, JKP

Concept of an ionizing time-domain matter-wave interferometer

We discuss the concept of an all-optical and ionizing matter-wave interferometer in the time domain. The proposed setup aims at testing the wave nature of highly massive clusters and molecules, and it will enable new precision experiments with a broad class of atoms, using the same laser system. The propagating particles are illuminated by three pulses of a standing ultraviolet laser beam, which detaches an electron via efficient single photon-absorption. Optical gratings may have periods as small as 80 nm, leading to wide diffraction angles for cold atoms and to compact setups even for very massive clusters. Accounting for the coherent and the incoherent parts of the particle-light interaction, we show that the combined effect of phase and amplitude modulation of the matter waves gives rise to a Talbot-Lau-like interference effect with a characteristic dependence on the pulse delay time.Comment: 25 pages, 5 figure

Novel Smartphone Interventions Improve Cognitive Flexibility and Obsessive-Compulsive Disorder Symptoms in Individuals with Contamination Fears.

One type of obsessive-compulsive disorder (OCD) is characterized by contamination fears and compulsive cleansing. Few effective treatments are available for this debilitating condition. Compulsive symptoms, such as excessive washing, are believed to be mediated by cognitive inflexibility-arguably the most striking cognitive impairment in OCD. In this study, we investigated the effects of two novel smartphone interventions on cognitive flexibility and OCD symptoms in healthy individuals with OCD-like contamination fears. In the first intervention, participants watched a brief video recording of themselves engaging in handwashing on a smartphone, four times a day, for a total of one week (N = 31). The second intervention was similar except that participants watched themselves repeatedly touching a disgust-inducing object (N = 31). In a third (control) "intervention", participants watched themselves performing sequential hand movements (N = 31). As hypothesized, the two smartphone interventions, unlike the control, improved cognitive flexibility; as assessed on the Intradimensional-Extradimensional Set Shifting task (a sensitive marker of cognitive flexibility). The two interventions, unlike the control, also improved OCD symptoms (measured with the Obsessive-Compulsive Inventory-Revised and Yale-Brown Obsessive-Compulsive Scale). Finally, we found high levels of adherence to the interventions. These findings have significant clinical implications for OCD

Contribution of solitons to enhanced rogue wave occurrence in shallow depths: a case study in the southern North Sea

The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform (NLFT) based on the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). At measurement sites where the propagation of waves can be described by the KdV equation, the solitons in the discrete nonlinear vKdV-NLFT spectrum correspond to physical solitons. We do not know whether this is the case at the considered measurement site. In this paper, we use the nonlinear spectrum to classify rogue wave and non-rogue wave time series. More specifically, we investigate if the discrete nonlinear spectra of measured time series with visible rogue waves differ from those without rogue waves. Whether or not the discrete part of the nonlinear spectrum corresponds to solitons with respect to the conditions at the measurement site is not relevant in this case, as we are not concerned with how these spectra change during propagation. For each time series containing a rogue wave, we were able to identify at least one soliton in the nonlinear spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were found to be smaller than the crest height of the corresponding rogue wave, and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, but the largest soliton was outstanding, with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards the enhanced probability of the occurrence of a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. These results suggest that soliton-like and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.</p

Experimentally induced and real-world anxiety have no demonstrable effect on goal-directed behaviour.

BACKGROUND: Goal-directed control guides optimal decision-making and it is an important cognitive faculty that protects against developing habits. Previous studies have found some evidence of goal-directed deficits when healthy individuals are stressed, and in psychiatric conditions characterised by compulsive behaviours and anxiety. Here, we tested if goal-directed control is affected by state anxiety, which might explain the former results. METHODS: We carried out a causal test of this hypothesis in two experiments (between-subject N = 88; within-subject N = 50) that used the inhalation of hypercapnic gas (7.5% CO2) to induce an acute state of anxiety in healthy volunteers. In a third experiment (N = 1413), we used a correlational design to test if real-life anxiety-provoking events (panic attacks, stressful events) are associated with impaired goal-directed control. RESULTS: In the former two causal experiments, we induced a profoundly anxious state, both physiologically and psychologically, but this did not affect goal-directed performance. In the third, correlational, study, we found no evidence for an association between goal-directed control, panic attacks or stressful life eventsover and above variance accounted for by trait differences in compulsivity. CONCLUSIONS: In sum, three complementary experiments found no evidence that anxiety impairs goal-directed control in human subjects.Research was funded by a Wellcome Trust Senior Investigator Award (TW Robbins 106431/Z/14/Z) and a Sir Henry Wellcome Postdoctoral Fellowship (CM Gillan 101521/Z/12/Z). CM Gillan is supported by a fellowship from MQ: transforming mental health (MQ16IP13). AB Brühl was supported by a fellowship from the Swiss National Science Foundation (SNF PASMP3-145749). FH Hezemans is supported by a Cambridge Trust Vice-Chancellor’s Award and Fitzwilliam College scholarship and was previously supported by an Erasmus scholarship. G Savulich was funded by The Wallitt Foundation and Eton College, with support from the NIHR Cambridge Biomedical Research Centre (BRC) Mental Health theme