Differentially passive circuits that switch and oscillate

The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and oscillate as interconnections of passive components with operational amplifiers (op-amps). The approach builds on recent results on dominance and p-passivity aimed at generalizing dissipativity theory to the analysis of non-equilibrium nonlinear systems. Our paper shows how those results apply to basic and well-known nonlinear circuit architectures. They illustrate the potential of dissipativity theory to design and analyze switching and oscillating circuits quantitatively, very much like their linear counterparts

Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach

Deflation is an efficient numerical technique for identifying new branches of steady state solutions to nonlinear partial differential equations. Here, we demonstrate how to extend deflation to discover new periodic orbits in nonlinear dynamical lattices. We employ our extension to identify discrete breathers, which are generic exponentially localized, time-periodic solutions of such lattices. We compare different approaches to using deflation for periodic orbits, including ones based on a Fourier decomposition of the solution, as well as ones based on the solution's energy density profile. We demonstrate the ability of the method to obtain a wide variety of multibreather solutions without prior knowledge about their spatial profile

A transfer matrix method for the analysis of fractal quantum potentials

The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory quantum mechanics for undergraduates. The reflection coefficients for both the fractal potential and the finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal has a self-similar structure associated with the fractal distribution of the potential

A modular synthetic device to calibrate promoters

In this contribution, a design of a synthetic calibration genetic circuit to characterize the relative strength of different sensing promoters is proposed and its specifications and performance are analyzed via an effective mathematical model. Our calibrator device possesses certain novel and useful features like modularity (and thus the possibility of being used in many different biological contexts), simplicity, being based on a single cell, high sensitivity and fast response. To uncover the critical model parameters and the corresponding parameter domain at which the calibrator performance will be optimal, a sensitivity analysis of the model parameters was carried out over a given range of sensing protein concentrations (acting as input). Our analysis suggests that the half saturation constants for repression, sensing and difference in binding cooperativity (Hill coefficients) for repression are the key to the performance of the proposed device. They furthermore are determinant for the sensing speed of the device, showing that it is possible to produce detectable differences in the repression protein concentrations and in turn in the corresponding fluorescence in less than two hours. This analysis paves the way for the design, experimental construction and validation of a new family of functional genetic circuits for the purpose of calibrating promoters.Comment: 24 pages, 11 figure

Optical nanofibers and spectroscopy

We review our recent progress in the production and characterization of tapered optical fibers with a sub-wavelength diameter waist. Such fibers exhibit a pronounced evanescent field and are therefore a useful tool for highly sensitive evanescent wave spectroscopy of adsorbates on the fiber waist or of the medium surrounding. We use a carefully designed flame pulling process that allows us to realize preset fiber diameter profiles. In order to determine the waist diameter and to verify the fiber profile, we employ scanning electron microscope measurements and a novel accurate in situ optical method based on harmonic generation. We use our fibers for linear and non-linear absorption and fluorescence spectroscopy of surface-adsorbed organic molecules and investigate their agglomeration dynamics. Furthermore, we apply our spectroscopic method to quantum dots on the surface of the fiber waist and to caesium vapor surrounding the fiber. Finally, towards dispersive measurements, we present our first results on building and testing a single-fiber bi-modal interferometer.Comment: 13 pages, 18 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: changed title, clarification of some points in the text, added references, replacement of Figure 13

An approach to assess flooding and erosion risk for open beaches in a changing climate

This paper examines the vulnerability to flooding and erosion of four open beach study sites in Europe. A framework for the quantitative estimation of present and future coastal flood and erosion risks is established using methods, data and tools from across a range of disciplines, including topographic and bathymetric data, climate data from observation, hindcast and model projections, statistical modelling of current and future climates and integrated risk analysis tools. Uncertainties in the estimation of future coastal system dynamics are considered, as are the consequences for the inland systems. Different implementations of the framework are applied to the study sites which have different wave, tidal and surge climate conditions. These sites are: Santander, Spain—the Atlantic Ocean; Bellocchio, Italy—the Adriatic Sea; Varna, Bulgaria—the Black Sea; and the Teign Estuary, UK—the northern Atlantic Ocean. The complexity of each system is first simplified by sub-division into coastal "impact units" defined by homogeneity in the local key forcing parameters: wave, wind, tide, river discharge, run-off, etc. This reduces the simulation to that of a number of simpler linear problems which are treated by applying the first two components of the Source–Pathway–Receptor–Consequence (S–P–R–C) approach. The case studies reveal the flexibility of this approach, which is found useful for the rapid assessment of the risks of flooding and erosion for a range of scenarios and the likely effectiveness of flood defences

Utilisation of an operative difficulty grading scale for laparoscopic cholecystectomy

Background A reliable system for grading operative difficulty of laparoscopic cholecystectomy would standardise description of findings and reporting of outcomes. The aim of this study was to validate a difficulty grading system (Nassar scale), testing its applicability and consistency in two large prospective datasets. Methods Patient and disease-related variables and 30-day outcomes were identified in two prospective cholecystectomy databases: the multi-centre prospective cohort of 8820 patients from the recent CholeS Study and the single-surgeon series containing 4089 patients. Operative data and patient outcomes were correlated with Nassar operative difficultly scale, using Kendall’s tau for dichotomous variables, or Jonckheere–Terpstra tests for continuous variables. A ROC curve analysis was performed, to quantify the predictive accuracy of the scale for each outcome, with continuous outcomes dichotomised, prior to analysis. Results A higher operative difficulty grade was consistently associated with worse outcomes for the patients in both the reference and CholeS cohorts. The median length of stay increased from 0 to 4 days, and the 30-day complication rate from 7.6 to 24.4% as the difficulty grade increased from 1 to 4/5 (both p < 0.001). In the CholeS cohort, a higher difficulty grade was found to be most strongly associated with conversion to open and 30-day mortality (AUROC = 0.903, 0.822, respectively). On multivariable analysis, the Nassar operative difficultly scale was found to be a significant independent predictor of operative duration, conversion to open surgery, 30-day complications and 30-day reintervention (all p < 0.001). Conclusion We have shown that an operative difficulty scale can standardise the description of operative findings by multiple grades of surgeons to facilitate audit, training assessment and research. It provides a tool for reporting operative findings, disease severity and technical difficulty and can be utilised in future research to reliably compare outcomes according to case mix and intra-operative difficulty

Glucosinolates, myrosinase hydrolysis products, and flavonols found in rocket (Eruca sativa and Diplotaxis tenuifolia)

Rocket species have been shown to have very high concentrations of glucosinolates and flavonols, which have numerous positive health benefits with regular consumption. In this review we highlight how breeders and processors of rocket species can utilize genomic and phytochemical research to improve varieties and enhance the nutritive benefits to consumers. Plant breeders are increasingly looking to new technologies such as HPLC, UPLC, LC-MS and GC-MS to screen populations for their phytochemical content to inform plant selections. Here we collate the research that has been conducted to-date in rocket, and summarise all glucosinolate and flavonol compounds identified in the species. We emphasize the importance of the broad screening of populations for phytochemicals and myrosinase degradation products, as well as unique traits that may be found in underutilized gene bank resources. We also stress that collaboration with industrial partners is becoming essential for long-term plant breeding goals through research

Transparent Boundary Condition for Oseen-Frank Model. Application for NLC Cells With Patterned Electrodes

In the present work a novel application of Transparent Boundary Conditions (TBC) to nematic liquid crystal cells (NLCC) with planar alignment and a patterned electrode is studied. This device is attracting great interest since it allows soliton steering by optically and externally induced waveguides. We employ the continuum Oseen-Frank theory to find the tilt and twist angle distributions in the cell under the one-constant approximation. The electric field distribution takes into account the whole 2D permittivity tensor for the transverse coordinates. Standard finite difference time domain methods together with an iterative method is applied to find an approximate solution to our coupled problem. A novel class of TBC is used to correctly define the boundary for both the distortion angle problem and the electric field distribution when using patterned electrodes. Thus, we achieve an important decrease of computational needs when solving this kind of problems and we are also capable of exploring weak anchoring conditions for NLCC.Orquín Serrano, I.; Vijande, J.; Villatoro Machuca, FR.; Ferrando, A.; Fernández De Córdoba Castellá, PJ.; Michinel Alvarez, H. (2015). Transparent Boundary Condition for Oseen-Frank Model. Application for NLC Cells With Patterned Electrodes. Journal of Physics: Conference Series. 605:0120281-01202811. doi:10.1088/1742-6596/605/1/012028S012028101202811605Peccianti, M., De Rossi, A., Assanto, G., De Luca, A., Umeton, C., & Khoo, I. C. (2000). Electrically assisted self-confinement and waveguiding in planar nematic liquid crystal cells. Applied Physics Letters, 77(1), 7-9. doi:10.1063/1.126859Peccianti, M., & Assanto, G. (2001). Signal readdressing by steering of spatial solitons in bulk nematic liquid crystals. Optics Letters, 26(21), 1690. doi:10.1364/ol.26.001690Peccianti, M., Conti, C., Assanto, G., De Luca, A., & Umeton, C. (2002). All-optical switching and logic gating with spatial solitons in liquid crystals. Applied Physics Letters, 81(18), 3335-3337. doi:10.1063/1.1519101Fratalocchi, A., Assanto, G., Brzdąkiewicz, K. A., & Karpierz, M. A. (2005). All-optical switching and beam steering in tunable waveguide arrays. Applied Physics Letters, 86(5), 051112. doi:10.1063/1.1857071Fratalocchi, A., Assanto, G., Brzdąkiewicz, K. A., & Karpierz, M. A. (2005). Optical multiband vector breathers in tunable waveguide arrays. Optics Letters, 30(2), 174. doi:10.1364/ol.30.000174Beeckman, J., Neyts, K., & Haelterman, M. (2006). Patterned electrode steering of nematicons. Journal of Optics A: Pure and Applied Optics, 8(2), 214-220. doi:10.1088/1464-4258/8/2/018Peccianti, M., Dyadyusha, A., Kaczmarek, M., & Assanto, G. (2008). Escaping Solitons from a Trapping Potential. Physical Review Letters, 101(15). doi:10.1103/physrevlett.101.153902Kivshar, Y. (2006). Bending light at will. Nature Physics, 2(11), 729-730. doi:10.1038/nphys452Alexe-Ionescu, A. L., Barberi, R., Barbero, G., & Giocondo, M. (1994). Anchoring energy for nematic liquid crystals: Contribution from the spatial variation of the elastic constants. Physical Review E, 49(6), 5378-5388. doi:10.1103/physreve.49.5378Allen, M. P., & Frenkel, D. (1988). Calculation of liquid-crystal Frank constants by computer simulation. Physical Review A, 37(5), 1813-1816. doi:10.1103/physreva.37.1813He, S. (2001). Iterative finite-difference method for calculating the distribution of a liquid-crystal director. Optical Engineering, 40(11), 2552. doi:10.1117/1.1411974Engquist, B., & Majda, A. (1977). Absorbing boundary conditions for the numerical simulation of waves. Mathematics of Computation, 31(139), 629-629. doi:10.1090/s0025-5718-1977-0436612-4Grote, M. J., & Keller, J. B. (1995). Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation. SIAM Journal on Applied Mathematics, 55(2), 280-297. doi:10.1137/s0036139993269266Hagstrom, T., Warburton, T., & Givoli, D. (2010). Radiation boundary conditions for time-dependent waves based on complete plane wave expansions. Journal of Computational and Applied Mathematics, 234(6), 1988-1995. doi:10.1016/j.cam.2009.08.050Baskakov, V. A., & Popov, A. V. (1991). Implementation of transparent boundaries for numerical solution of the Schrödinger equation. Wave Motion, 14(2), 123-128. doi:10.1016/0165-2125(91)90053-qLubich, C., & Schädle, A. (2002). Fast Convolution for Nonreflecting Boundary Conditions. SIAM Journal on Scientific Computing, 24(1), 161-182. doi:10.1137/s1064827501388741Kuska, J.-P. (1992). Absorbing boundary conditions for the Schrödinger equation on finite intervals. Physical Review B, 46(8), 5000-5003. doi:10.1103/physrevb.46.5000Di Menza, L. (1996). Absorbing boundary conditions on a hypersurface for the Schrödinger equation in a half-space. Applied Mathematics Letters, 9(4), 55-59. doi:10.1016/0893-9659(96)00051-1Schädle, A. (2002). Non-reflecting boundary conditions for the two-dimensional Schrödinger equation. Wave Motion, 35(2), 181-188. doi:10.1016/s0165-2125(01)00098-1Arnold, A., Ehrhardt, M., & Sofronov, I. (2003). Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability. Communications in Mathematical Sciences, 1(3), 501-556. doi:10.4310/cms.2003.v1.n3.a7Lindquist, J. M., Neta, B., & Giraldo, F. X. (2012). High-order non-reflecting boundary conditions for dispersive waves in polar coordinates using spectral elements. Applied Mathematics and Computation, 218(12), 6666-6676. doi:10.1016/j.amc.2011.12.023Sun, Z., Wu, X., Zhang, J., & Wang, D. (2012). A linearized difference scheme for semilinear parabolic equations with nonlinear absorbing boundary conditions. Applied Mathematics and Computation, 218(9), 5187-5201. doi:10.1016/j.amc.2011.10.083Hadley, G. R. (1991). Transparent boundary condition for beam propagation. Optics Letters, 16(9), 624. doi:10.1364/ol.16.000624Hadley, G. R. (1992). Transparent boundary condition for the beam propagation method. IEEE Journal of Quantum Electronics, 28(1), 363-370. doi:10.1109/3.119536Beeckman, J., Chałubinska, K., & Neyts, K. (2006). Lateral Light Propagation in SSFLC Devices and Thermal Optical Nonlinearities. Ferroelectrics, 344(1), 225-231. doi:10.1080/00150190600968348Peccianti, M., Dyadyusha, A., Kaczmarek, M., & Assanto, G. (2006). Tunable refraction and reflection of self-confined light beams. Nature Physics, 2(11), 737-742. doi:10.1038/nphys42