Wide Range Of Realistic Parameters Research Articles

Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights

We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss--Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of realistic parameters, corresponding to the requirements of numerical integration to an accuracy of about 100 to 100000 bits. Our algorithm combines the summation by rectangular splitting of several types of expansions in terms of hypergeometric series with a fixed-point implementation of Bonnet's three-term recurrence relation. We then compute rigorous enclosures of the Gauss--Legendre nodes and weights using the interval Newton method. We provide rigorous error bounds for all steps of the algorithm. The approach is validated by an implementation in the Arb library, which achieves order-of-magnitude speedups over previous code for computing Gauss--Legendre rules suitable for precisions in the thousands of bits.

A robust quantum receiver for phase shift keyed signals

The impossibility of perfectly discriminating non-orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes. We propose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector. We provide a detailed analysis of the influence of excess noise and technical imperfections on the average error probability. The results demonstrate the receiver’s robustness and show that it can outperform any classical receiver over a wide range of realistic parameters.

Asymmetric Coulomb fluids at randomly charged dielectric interfaces: anti-fragility, overcharging and charge inversion.

We study the distribution of multivalent counterions next to a dielectric slab, bearing a quenched, random distribution of charges on one of its solution interfaces, with a given mean and variance, both in the absence and in the presence of a bathing monovalent salt solution. We use the previously derived approach based on the dressed multivalent-ion theory that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework. The presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the density of multivalent counterions in its vicinity. In the counterion-only model (with no monovalent salt ions), the surface disorder generates an additional logarithmic attraction potential and thus an algebraically singular counterion density profile at the surface. This behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact-value theorem, reflecting the anti-fragility effects of the disorder that drive the system towards a more "ordered" state. In the presence of an interfacial dielectric discontinuity, depleting the counterion layer at the surface, the charge disorder still generates a much enhanced counterion density further away from the surface. Likewise, the charge inversion and/or overcharging of the surface occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder. Overall, the presence of quenched surface charge disorder leads to sizable effects in the distribution of multivalent counterions in a wide range of realistic parameters and typically within a distance of a few nanometers from the charged surface.

Efficient Biologically Inspired Photocell Enhanced by Delocalized Quantum States

Artificially implementing the biological light reactions responsible for the remarkably efficient photon-to-charge conversion in photosynthetic complexes represents a new direction for the future development of photovoltaic devices. Here, we develop such a paradigm and present a model photocell based on the nanoscale architecture and molecular elements of photosynthetic reaction centers. Quantum interference of photon absorption and emission induced by the dipole-dipole interaction between molecular excited states guarantees an enhanced light-to-current conversion and power generation for a wide range of electronic, thermal, and optical parameters for optimized dipolar geometries. This result opens a promising new route for designing artificial light-harvesting devices inspired by biological photosynthesis and quantum technologies.

Dynamics of the Biennial Oscillation in the Equatorial Indian and Far Western Pacific Oceans

Abstract Many investigators have noted strong biennial atmospheric and oceanic variability, phase-locked to the calendar year, over the equatorial Indian and Pacific Oceans. A simple air–sea interaction theory suggests that biennial oscillations in the far western equatorial Pacific (120°–140°E) may originate from an air–sea interaction instability involving the mean seasonal wind cycle and evaporation. Over a wide range of realistic parameters the instability grows rapidly and is phase-locked to the calendar year in a similar way to the observations. Crucial to the mechanism are that the anomalous equatorial surface wind response is westerly under anomalous deep convection, that it lags the convection by at least 1 month, and that the zonal seasonal wind has a strong 12-month cycle. No such air–sea interaction instability is possible in the equatorial Indian Ocean because the water is either too cold for deep convection most of the year (western equatorial Indian Ocean, 40°–60°E) or the wind is westerly ...

The effect of functional response on stability of a grazer population on a landscape

The dynamics of interacting consumer and resource populations is one of the most thoroughly studied problems of theoretical population biology. Among the key results from the study of simple mathematical models of interacting populations is that the Holling Type 2 functional response tends to be unstable for a wide range of realistic parameters. Functional responses such as Holling Type 3, which might be thought of as implicitly incorporating the existence of consumer refuges, are more stable than the Type 2. We studied consumer—resource models with these different functional responses on a landscape level by modeling grazers that can disperse across a space of patchily distributed grass resources. For certain assumptions concerning the movement of grazers on the landscape, the effect of these functional responses on stability is reversed; the Holling Type 2 functional response confers greater stability. The reason for this apparently paradoxical result is that the Holling Type 2 functional response allows grazers to graze individual grass patches to lower levels than Type 3, as the energy balance remains favorable for grazing at lower grass biomasses. However, this local overexploitation leads the grazers to be slower in reaching areas of the landscape where resource densities are higher. It decreases the likelihood that the resource will be overexploited over the whole landscape simultaneously, which results in a stronger tendency towards system stability. It appears, then, that consumer overexploitation of resources locally may contribute to lower stability.

The B�ttiker-Landauer model generalized

Buttiker and Landauer studied scattering off an oscillating rectangular barrier in order to shed light on the time aspects of tunneling. The expression for the traversal time resulting from this study is controversial. In addition, doubts have recently been expressed on technical aspects of their work. In an attempt to clarify these issues, we investigate a generalization of their model to arbitrary oscillating barriers,V(x, t)=V0(x)+V1(x)cos ωt. In the process, we confirm that Buttiker and Landauer's work is technically sound. However, we show, by several examples, that no direct general relation exists between the characteristic frequency of an oscillating barrier and the duration of the tunneling process. For a wide range of realistic parameters this characteristic frequency does not even exist.