Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The $E\otimes\beta$ system models the coupling of a two-level electronic system, or qubit, to a single oscillator mode, while the $E\otimes\epsilon$ models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the $E\otimes\beta$ system, the ground states of the $E\otimes\epsilon$ model always exhibit entanglement. For the $E\otimes\beta$ case we aim to clarify results from previous work, alluding to a link between the ground state entanglement characteristics and a bifurcation of a fixed point in the classical analogue. In the $E\otimes\epsilon$ case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.Comment: 11 pages, 9 figures, comments welcome; 2 references adde

Aircraft requirements for low/medium density markets

A study was conducted to determine the demand for and the economic factors involved in air transportation in a low and medium density market. The subjects investigated are as follows: (1) industry and market structure, (2) aircraft analysis, (3) economic analysis, (4) field surveys, and (5) computer network analysis. Graphs are included to show the economic requirements and the aircraft performance characteristics

Photonic Clusters

We show through rigorous calculations that dielectric microspheres can be organized by an incident electromagnetic plane wave into stable cluster configurations, which we call photonic molecules. The long-range optical binding force arises from multiple scattering between the spheres. A photonic molecule can exhibit a multiplicity of distinct geometries, including quasicrystal-like configurations, with exotic dynamics. Linear stability analysis and dynamical simulations show that the equilibrium configurations can correspond with either stable or a type of quasi-stable states exhibiting periodic particle motion in the presence of frictional dissipation.Comment: 4 pages, 3 figure

A minimal model for chaotic shear banding in shear-thickening fluids

We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A

Who are you talking to? The role of addressee identity in utterance comprehension

Issue online: 30 March 2020Experimental evidence suggests that speaker and addressee quickly adapt to each other from the earliest moments of sentence processing, and that interlocutor-related information is rapidly integrated with other sources of nonpragmatic information (e.g., semantic, morphosyntactic, etc.). These findings have been taken as support for one-step models of sentence comprehension. The results from the present eventrelated potential study challenge this theoretical framework providing a case where discourse level information is integrated only at a late stage of processing, when morphosyntactic analysis has been already initiated. We considered the case of Basque allocutive agreement, where information about addressee gender is encoded in verbal inflection. Two different types of Basque grammatical violations were presented together with the corresponding control conditions: one could be detected based on a morphosyntactic mismatch (person agreement violation), while the other could be detected only if the addressee's gender was considered (allocutive violation). Morphosyntactic violations elicited greater N400 effects followed by P600 effects, while allocutive violations elicited only P600 effects. These results provide new constraints to one-step accounts as they represent a case where speakers do not immediately adjust to the addressee's perspective. We propose that the relevance of discourse-level information might be a crucial variable to reconcile the dichotomy between one- and two-step models.Horizon 2020 Framework Programme, Grant/Award Number: H2020-MSCAIF- 2018-837228; Fundación BBVA, Grant/ Award Number: IN[18]_HMS_LIN_0058; Ministerio de Economía y Competitividad, Grant/Award Number: IJCI-2016-27702, PSI2014-54500, RYC 2017-22015 and SEV-2015-490; Eusko Jaurlaritza, Grant/ Award Number: PI_2015_1_25; Gipuzkoa Fellowship Program, Grant/Award Number: FFI2016-76432-P. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 83722

Potential For Power: A Symposium On The Prospects For Power From Currently Unconventional Energy Sources

The wave energy arriving on the west coast of the United Kingdom represents a very substantial energy resource, amounting on average to more than twice the present installed capacity of the CEGB. Recent, comprehensive, studies by the CEGB (1) (2) and the National Engineering Laboratory (3) suggest that although there is no obvious technical reason for being unable ultimately to harness much of this energy, and many methods have been proposed, there are still considerable uncertainties over the choice of wave power system and its economics. Wave power does show sufficient promise however to have been made the subject of serious studies supported by the CEGB and the Department of Energy (4). In this Paper the potential of wave power and some of the more promising methods of harnessing it are discussed, together with an appreciation of some of the many technical and engineering problems which still need to be examined, and a discussion of the impact of wave power on the environment. By considering the results of recent research and their impact on wave power economics it is argued that wave power could be exploited to conserve fossil fuels but is unlikely to be competitive with nuclear power

Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

General Stability Analysis of Synchronized Dynamics in Coupled Systems

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on the master stability function and Gershgorin disc theory, to yield constraints on the coupling strengths to ensure the stability of synchronized dynamics. Systems with specific coupling schemes are used as examples to illustrate our general method.Comment: 8 pages, 1 figur

In-reach specialist nursing teams for residential care homes : uptake of services, impact on care provision and cost-effectiveness

Background: A joint NHS-Local Authority initiative in England designed to provide a dedicated nursing and physiotherapy in-reach team (IRT) to four residential care homes has been evaluated.The IRT supported 131 residents and maintained 15 'virtual' beds for specialist nursing in these care homes. Methods: Data captured prospectively (July 2005 to June 2007) included: numbers of referrals; reason for referral; outcome (e.g. admission to IRT bed, short-term IRT support); length of stay in IRT; prevented hospital admissions; early hospital discharges; avoided nursing home transfers; and detection of unrecognised illnesses. An economic analysis was undertaken. Results: 733 referrals were made during the 2 years (range 0.5 to 13.0 per resident per annum)resulting in a total of 6,528 visits. Two thirds of referrals aimed at maintaining the resident's independence in the care home. According to expert panel assessment, 197 hospital admissions were averted over the period; 20 early discharges facilitated; and 28 resident transfers to a nursing home prevented. Detection of previously unrecognised illnesses accounted for a high number of visits. Investment in IRT equalled £44.38 per resident per week. Savings through reduced hospital admissions, early discharges, delayed transfers to nursing homes, and identification of previously unrecognised illnesses are conservatively estimated to produce a final reduction in care cost of £6.33 per resident per week. A sensitivity analysis indicates this figure might range from a weekly overall saving of £36.90 per resident to a 'worst case' estimate of £2.70 extra expenditure per resident per week. Evaluation early in implementation may underestimate some cost-saving activities and greater savings may emerge over a longer time period. Similarly, IRT costs may reduce over time due to the potential for refinement of team without major loss in effectiveness. Conclusion: Introduction of a specialist nursing in-reach team for residential homes is at least cost neutral and, in all probability, cost saving. Further benefits include development of new skills in the care home workforce and enhanced quality of care. Residents are enabled to stay in familiar surroundings rather than unnecessarily spending time in hospital or being transferred to a higher dependency nursing home setting