Bifurcations in a delayed differential-algebraic plankton economic system

This paper considers a phytoplankton-zooplankton bio-economic system with delay and harvesting, which is described by differential-algebraic equations. Local stability analysis of the system without delay reveals that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest is taken into account, furthermore, a state feedback controller is designed to stabilize the system at the interior equilibrium. Then, we show that delay, which is considered in the toxic liberation, can induce stability switches, such that the positive equilibrium switches from stability to instability, to stability again and so on. Finally, some numerical simulations are performed to justify analytical findings.     

Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III

In this paper we study a generalized Gause model with prey harvesting and a generalized Holling response function of type III: . The goal of our study is to give the bifurcation diagram of the model. For this we need to study saddle-node bifurcations, Hopf bifurcation of codimension 1 and 2, heteroclinic bifurcation, and nilpotent saddle bifurcation of codimension 2 and 3. The nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram. The Hopf bifurcation is studied by means of a generalized Liénard system, and for b=0 we discuss the potential integrability of the system. The nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4. But because it occurs with an invariant line, the effective highest codimension is 3. We develop normal forms (in which the invariant line is preserved) for studying of the nilpotent saddle bifurcation. For b=0, the reversibility of the nilpotent saddle is discussed. We study the type of the heteroclinic loop and its cyclicity. The phase portraits of the bifurcations diagram (partially conjectured via the results obtained) allow us to give a biological interpretation of the behavior of the two species.     

Almost periodic solution for Nicholson’s blowflies model with patch structure and linear harvesting terms

In this paper, we study the existence and exponential convergence of positive almost periodic solutions for a class of Nicholson’s blowflies model with patch structure and multiple linear harvesting terms. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system converge locally exponentially to a positive almost periodic solution. Moreover, we give some examples and numerical simulations to illustrate our main results.     

Stable coexistence mediated by specialist harvesting in a two zooplankton–phytoplankton system

This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings.     

Resonance energy transfer: Beyond the limits

In pursuit of a better understanding of how electronic excitation migrates within complex structures, the concept of resonance energy transfer is being extended and deployed in a wide range of applications. Utilizing knowledge of the quantum interactions that operate in natural photosynthetic systems, wide‐ranging molecular and solid‐state materials are explored in the cause of more efficient solar energy harvesting, while advances in theory are paving the way for the development and application of fundamentally new mechanisms. In this review, an introduction to the underlying processes that cause singlet‐singlet and triplet‐triplet energy transfer leads into a discussion of how a new conception of these fundamental processes has emerged over recent years. Illustrative examples relevant to laser science and photonics are described, including photosynthetic light‐harvesting, light‐activated sensors, processes of cooperative and accretive energy pooling and quantum cutting in rare earth‐doped crystals, and incoherent triplet‐triplet energy upconversion in molecular solutions.     

Versatile Bisethynyl[60]fulleropyrrolidine Scaffolds for Mimicking Artificial Light‐Harvesting Photoreaction Centers

Fullerene‐based tetrads, triads, and dyads are presented in which [60]fulleropyrrolidine synthons are linked to an oligo(p‐phenyleneethynylene) antenna at the nitrogen atom and to electron‐donor phenothiazine (PTZ) and/or ferrocene (Fc) moieties at the α carbon of the pyrrolidine cycle through an acetylene spacer. Cyclic voltammetry and UV/ Vis absorption spectra evidence negligible ground‐state electronic interactions among the subunits. By contrast, strong excited‐state interactions are detected upon selective light irradiation of the antenna (UV) or of the fullerene scaffold (Vis). When only PTZ is present as electron donor, photoinduced electron transfer to the fullerene unit is unambiguously detected in benzonitrile, but this is not the case when Fc is part of the multicomponent system. These results suggest that Fc is a formidable energy transfer quencher and caution should be used in choosing it as electron donor to promote efficient charge separation in multicomponent arrays.     

On the efficiency of energy harvesting using vortex-induced vibrations of cables

Many technologies based on fluid–structure interaction mechanisms are being developed to harvest energy from geophysical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using vortex-induced vibrations (VIV) of cables is addressed in this paper, through two reference configurations: (i) a long tensioned cable with periodically-distributed harvesters and (ii) a hanging cable with a single harvester at its upper extremity. After validation against either direct numerical simulations or experiments, an appropriate reduced-order wake-oscillator model is used to perform parametric studies of the impact of the harvesting parameters on the efficiency. For both configurations, an optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically-mounted rigid cylinder. The variability of the efficiency is studied in light of the fundamental properties of each configuration, i.e. body flexibility and gravity-induced spatial variation of the tension. In the periodically-distributed harvester configuration, it is found that the standing-wave nature of the vibration and structural mode selection plays a central role in energy extraction. In contrast, the efficiency of the hanging cable is essentially driven by the occurrence of traveling wave vibrations.     

Zeolitic imidazolate framework-67 (ZIF-67) rhombic dodecahedrons as full-spectrum light harvesting photocatalyst for environmental remediation

The inferior utilization efficiency of light is the main obstacle to the practical application of traditional photocatalysts such as TiO₂ and ZnO. In this regard, the development of novel photocatalysts with the capability of harvesting full spectrum light (from ultraviolet (UV) to near-infrared (NIR)) energy is a promising solution for solar energy conversion and environmental remediation. Here, we report the discovery of a single material that can harvest UV, visible (VIS), and NIR radiations to decompose heavy metal contaminants in aqueous solution. Zeolitic imidazolate framework-67 (ZIF-67) rhombic dodecahedrons were synthesized through a facile solution approach and employed in the reduction of Cr(VI) under UV−VIS−NIR pulsed laser irradiation, which was generated from the fundamental, second and third harmonics of Nd:YAG laser, respectively. The nanostructures showed efficient Cr(VI) reduction under UV, VIS and NIR laser irradiation and the measured reduction efficiency (%) was 71.22%, 69.52%, and 40.79%, respectively after 120 min. A possible explanation for the photocatalytic activity in Cr(VI) reduction was proposed. This is the first study of its kind where pulsed laser and ZIF-67 rhombic dodecahedrons capable of harvesting full spectrum light energy have been employed for the removal of Cr(VI) from water. The extraordinary capacity of harvesting full-spectrum light and long-term stability make ZIF-67 a potential photocatalyst for environmental remediation.     

Efficient calculation of open quantum system dynamics and time‐resolved spectroscopy with distributed memory HEOM (DM‐HEOM)

Time‐ and frequency‐resolved optical signals provide insights into the properties of light‐harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the complex. The hierarchical equations of motion (HEOM) provide a unifying theory, which allows one to study the combined effects of system‐environment dissipation and non‐Markovian memory without making restrictive assumptions about weak or strong couplings or separability of vibrational and electronic degrees of freedom. With increasing system size the exact solution of the open quantum system dynamics requires memory and compute resources beyond a single compute node. To overcome this barrier, we developed a scalable variant of HEOM. Our distributed memory HEOM, DM‐HEOM, is a universal tool for open quantum system dynamics. It is used to accurately compute all experimentally accessible time‐ and frequency‐resolved processes in light‐harvesting molecular complexes with arbitrary system‐environment couplings for a wide range of temperatures and complex sizes. © 2018 Wiley Periodicals, Inc.