OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Partners for the E(1420)

We show that there is good evidence that the K′ and E mesons form part of a 0^?+ nonet, and discuss possible consequences for ψ and ψ′ decays.     

Long-term retention of ice-nucleating active Pseudomonas fluorescens by overwintering colorado potato beetles

Ice nucleating-active Pseudomonas fluorescens F264C was fed to Colorado potato beetles to determine bacterial retentioin in the beetle gut and its effect on the cold hardiness of this insect pest. The bacrterium was present in beetles recovered after overwintering in the field, seven months after their exposure to P. fluorescens. Retention was evident not only in the detection of the P. fluorescens ice nucleating gene, inaW, in bacterial cultures from beetle guts but also in the elevated supercooling points of some treated beetles.     

Breakdown of stabilization of atoms interacting with intense, high-frequency laser pulses

An analysis of the influence of the magnetic field of an intense, high-frequency laser pulse on the stabilization of an atomic system is presented. We demonstrate that at relatively modest intensities the magnetic field can significantly alter the dynamics of the system. In particular, a breakdown of stabilization occurs, thereby restricting the intensity regime in which the atom is relatively stable against ionization. Counterpropagating pulses do not negate the detrimental effects of the magnetic field. We compare our quantum mechanical results with classical Monte Carlo simulations.     

Exciplex Formation and Excited State Deactivation of Difluoroborondipyrromethene (Bodipy) Dyads

Two series of geometrically‐related dyads are discussed based on the difluoroborondipyrromethene (Bodipy) unit, and incorporating covalently attached hydroquinone/quinone groups. These units are anchored directly, or via a phenylene spacer, to the Bodipy core at the meso position in one series ( BD‐MHQ , BD‐MQ , BD‐MPHQ , BD‐MPQ ), but for the second series the attachment site is the 2‐position ( BD‐SHQ , BD‐SQ , BD‐SPHQ , BD‐SPQ ). The compounds show various levels of fluorescence depending on the oxidation state of the appended group and the substitution pattern. In non‐polar solvents such as toluene, diethyl ether and dichlorobenzene, the S₁ state deactivation of the Bodipy unit in BD‐SPQ and BD‐MPQ is dominated by ^{1, 3}exciplex formation, which has not been reported for Bodipy derivatives so far. In the latter molecule, the decay of the exciplex is divided between population of the Bodipy triplet state (13 %–21 %) and ground state reformation. This partitioning is not seen for the side‐on substituted derivative, BD‐SPQ , and only ground state reformation is observed following decay of the exciplex. This difference in behavior is explained by the radical‐pair inter‐system‐crossing mechanism, which more effectively operates in BD‐MPQ because of the orthogonality of the donor‐acceptor units. In the more polar solvent CH₃CN all the quinone derivatives show fast formation of the charge‐separated state (k_CS) followed by slower charge recombination (k_CR). The ratio k_CS/k_CR≤80.     

THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Probing the Rotational Dynamics of meso‐(2‐Substituted)aryl Substituents in A2B‐Type Subporphyrins

A₂B‐type B‐methoxy subporphyrins 3 a – g and B‐phenyl subporphyrins 7 a – c , e , g bearing meso‐(2‐substituted)aryl substituents are synthesized, and their rotational dynamics are examined through variable‐temperature (VT) ¹H NMR spectroscopy. In these subporphyrins, the rotation of meso‐aryl substituents is hindered by a rationally installed 2‐substituent. The rotational barriers determined are considerably smaller than those reported previously for porphyrins. Comparison of the rotation activation parameters reveals a variable contribution of ΔH^≠ and ΔS^≠ in ΔG^≠. 2‐Methyl and 2‐ethyl groups of the meso‐aryl substituents in subporphyrins 3 e , 3 f , and 7 e induce larger rotational barriers than 2‐alkoxyl substituents. The rotational barriers of 3 g and 7 g are reduced by the presence of the 4‐dibenzylamino group owing to its ability to stabilize the coplanar rotation transition state electronically. The smaller rotational barriers found for B‐phenyl subporphyrins than for B‐methoxy subporphyrins indicate a negligible contribution of S_N1‐type heterolysis in the rotation of meso‐aryl substituents.