Yang-Baxter equation for the asymmetric eight-vertex model

In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis clarify the reason both manifolds need to share a universal invariant. We also show that the free-fermion condition implies three distinct classes of integrable models.Comment: Latex, 12 pages, 1 figur

On the entanglement entropy for a XY spin chain

The entanglement entropy for the ground state of a XY spin chain is related to the corner transfer matrices of the triangular Ising model and expressed in closed form.Comment: 4 pages, 2 figure

Dynamics of lattice spins as a model of arrhythmia

We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.Comment: 17 pages, revtex, 3 figure

Wave-train induced unpinning of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.Comment: Published versio

Sustaining municipal parks in an era of neoliberal austerity: The contested commercialisation of Gunnersbury Park

This paper analyses a potentially path shaping moment for the UK’s public parks by analysing a pivotal case study of park neoliberalisation. Like many municipal parks, Gunnersbury Park in West London is experiencing the effects of local government budget cuts. Governance, policy and physical changes have been introduced to reduce dependence on public funding and the result is a more commercially oriented park. This case is used to better understand how the period of neoliberal austerity 2010-2020 reshaped municipal parks. The paper highlights concerns over the transparency and accountability of the social enterprise that now manages Gunnersbury Park. It also shows how neoliberalisation and commercialisation are manifested in the park landscape: free events are replaced with ticketed ones, spaces for sport are transformed into bookable facilities, cafes are taken over by corporate chains and playgrounds are supplemented with paid entry alternatives. One of the main consequences is the financial and symbolic exclusion of those unable or unwilling to pay. The paper explores who has contested the recent changes, and why. Opponents are dismissed as idealistic NIMBYs but, by refusing to accept the post-political inevitability of park neoliberalisation, they are helping to ensure Gunnersbury Park’s remains a public and open space. The case is contextualised by situating it within a review of new park governance arrangements across London, and by comparing neoliberalisation processes here with those affecting New York parks. Ultimately, the research highlights the pitfalls of shifting away from the public funding and public management of municipal parks.

Ordering in Two-Dimensional Ising Models with Competing Interactions

We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space of three Ising couplings are analyzed. In particular, incommensurate phases occurring only at non-equal diagonal couplings, are predicted. We also analyze a spin-pseudospin model comprised of the quantum Ising model coupled to XY spin chains in a particular region of interactions, corresponding to the Ising sector's super-antiferromagnetic (SAF) ground state. The spin-SAF transition in the coupled Ising-XY model into a phase with co-existent SAF Ising (pseudospin) long-range order and a spin gap is considered. Along with destruction of the quantum critical point of the Ising sector, the phase digram of the Ising-XY model can also demonstrate a re-entrance of the spin-SAF phase. A detailed study of the latter is presented. The mechanism of the re-entrance, due to interplay of interactions in the coupled model, and the conditions of its appearance are established. Applications of the spin-SAF theory for the transition in the quarter-filled ladder compound NaV2O5 are discussed.Comment: Minor revisions and refs. added; published version of the invited paper in a special issue of "Low Temp. Physics

Mechanisms of vortices termination in the cardiac muscle

We propose a solution to a long standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.The research leading to the results has received funding from Max Planck Gesellschaft, the European Community Seventh Framework Pro- gramme FP7/2007-2013 under Grant Agreement 17 No. HEALTH-F2-2009-241526, EUTrigTreat (DH, TB, SB, VIK, SL), and from EPSRC (UK) grant EP/I029664 (VNB).We also acknowledge support from the German Federal Ministry of Education and Research (BMBF) (project FKZ 031A147, GO-Bio), the German Research Foundation (DFG) (Collaborative Research Centres SFB 1002 Project C3 and SFB 937 Project A18), the Ger- man Center for Cardiovascular Research (DZHK e.V.) (DH, TB, SB, VIK, SL), Science & Engineering Research Board of Department of Science & Technology, Govern- ment of India (TKS), EPSRC (UK) grant EP/N014391 (VNB) and U.S. NIH Grant No. R01HL089271 (NFO)

Mechanisms of vortices termination in the cardiac muscle

We propose a solution to a long standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.The research leading to the results has received funding from Max Planck Gesellschaft, the European Community Seventh Framework Pro- gramme FP7/2007-2013 under Grant Agreement 17 No. HEALTH-F2-2009-241526, EUTrigTreat (DH, TB, SB, VIK, SL), and from EPSRC (UK) grant EP/I029664 (VNB).We also acknowledge support from the German Federal Ministry of Education and Research (BMBF) (project FKZ 031A147, GO-Bio), the German Research Foundation (DFG) (Collaborative Research Centres SFB 1002 Project C3 and SFB 937 Project A18), the Ger- man Center for Cardiovascular Research (DZHK e.V.) (DH, TB, SB, VIK, SL), Science & Engineering Research Board of Department of Science & Technology, Govern- ment of India (TKS), EPSRC (UK) grant EP/N014391 (VNB) and U.S. NIH Grant No. R01HL089271 (NFO)

Calculation of the Coherent Synchrotron Radiation Impedance from a Wiggler

Most studies of Coherent Synchrotron Radiation (CSR) have only considered the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter $K$. After an appropriate scaling, the results can be expressed in terms of universal functions, which are independent of $K$. Analytical asymptotic results are obtained for the wakefield in the limit of large and small distances, and for the impedance in the limit of small and high frequencies.Comment: 10 pages, 8 figure