MATHEMATICAL STUDY OF A PEST CONTROL MODEL INCORPORATING STERILE INSECT TECHNIQUE

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results.     

Nuclear triaxiality in the A ∼ 160–170 mass region: the story so far

Research in nuclear triaxial deformation has revealed many exciting facts and figures over the last one and a half-decades. Although wobbling motion of nuclei was experimentally discovered at the beginning of the last decade, after almost 25 years of its prediction by Bohr and Mottelson, efforts are still being put to understand this rare nuclear phenomenon in greater detail. The concept of transverse wobbling is one such recent attempt which successfully explains the evolution of experimentally observed wobbling frequency with spin. The population of triaxial strongly deformed (TSD) bands in the A ～160–170 region is favoured for which neutron number (N=92 or 94) is a topic of current debate. Experimental efforts are being put following Bengtsson’s calculations which indicate that the elevated yrast lines for N=92 isotones favour TSD population. In A ～170 mass region, the ambiguity over the real character of certain strongly deformed bands has recently been removed by extensive experimental and theoretical efforts, and the bands have now been firmly established as either enhanced deformed (ED) or superdeformed (SD).     

ISOLATION OF UNIQUE DIMER SPECTRA OF DYES FROM THE COMPOSITE SPECTRA OF AGGREGATED SOLUTIONS

Abstract— Aggregation of fluorescein, eosin and rose bengal in aqueous solutions has been studied. Mathematical expressions are derived to calculate the monomer mole fractions in moderately and highly concentrated solutions. The average values of the dimer dissociation constant, K_d , for fluorescein, eosin and rose bengal in aqueous solutions at pH 12 are 0.20, 9.0×10^-3 and 40 × 10^-3 moles/l respectively. A method is developed here to isolate the dimer spectrum from the composite spectrum. The uniqueness of this method is established by comparison with other known methods. The dimer spectra of all the three dyes are reported.     

A comparative study on dual colour soft aperture cascaded second-order mode-locking with different nonlinear optical crystals

A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.     

NONVANISHING OF CONFORMAL BLOCKS DIVISORS ON $$ {\overline{\mathrm{M}}}_{0,n} $$

We introduce and study the problem of finding necessary and sufficient conditions under which a conformal blocks divisor on \( {\overline{\mathrm{M}}}_{0,n} \) is nonzero, solving the problem completely for \( \mathfrak{s}{\mathfrak{l}}_2 \). We give necessary nonvanishing conditions in type A, which are sufficient when theta and critical levels coincide. We also show divisors are subject to additive identities, reflecting a decomposition of the weights and level.     

DIFFUSION INDUCED SHIFT OF BIFURCATION POINT IN A MANGROVE ECOSYSTEM FOOD‐CHAIN MODEL WITH HARVESTING

Abstract The present paper deals with a detritus‐based food‐chain model within a mangrove ecosystem. The top predator (mainly fish) is assumed to have a commercial value and undergoes harvesting. Stability and bifurcation behavior of the model is studied and a threshold harvest rate is obtained. Next we introduce environmental nonhomogenity into the model equation. The resulting reaction diffusion system is investigated, and the criteria for supercritical Hopf bifurcation is obtained using the method of Lyapunov first coefficient. A comparison of the critical harvest rates under the homogeneous and the nonhomogeneous context is performed both analytically and numerically.     

Efficient yellow beam generation by intracavity sum frequency mixing in DPSS Nd:YVO4 laser

We present our studies on dual wavelength operation using a single Nd:YVO₄ crystal and its intracavity sum frequency generation by considering the influence of the thermal lensing effect on the performance of the laser. A KTP crystal cut for type-II phase matching was used for intracavity sum frequency generation in the cavity at an appropriate location for efficient and stable yellow output power. More than 550 mW of stable CW yellow-orange beam at 593.5 nm with beam quality parameter (M ²) ～4. 3 was obtained. The total pump to yellow beam conversion efficiency was estimated to be 3.83%.     

Evolution of giant dipole resonance width at low temperatures – New perspectives

High energy photons from the decay of giant dipole resonances (GDR) built on excited states provide an excellent probe in the study of nuclear structure properties, damping mechanisms etc., at finite temperatures. The dependence of GDR width on temperature (T) and angular momentum (J) has been the prime focus of many experimental and theoretical studies for the last few decades. The measured GDR widths for a wide range of nuclei at temperatures (1.5 < T < 2.5 MeV) and spins (upto fission limit) were well described by the thermal shape fluctuation model (TSFM). But, at low temperatures (T < 1.5 MeV) there are large discrepancies between the existing theoretical models. The problem is compounded as there are very few experimental data in this region. At Variable Energy Cyclotron Centre, Kolkata, a programme for the systematic measurement of GDR width at very low temperatures has been initiated with precise experimental techniques. Several experiments have been performed by bombarding 7–12 MeV/nucleon alpha beam on various targets (⁶³Cu, ¹¹⁵In and ¹⁹⁷Au) and new datasets have been obtained at low temperatures (T < 1.5 MeV) and at very low spins ( $J < 20 \hbar $ ). The TSFM completely fails to represent the experimental data at these low temperatures in the entire mass range. In fact, the GDR width appears to be constant at its ground state value until a critical temperature is reached and subsequently increases thereafter, whereas the TSFM predicts a gradual increase of GDR width from its ground state value for T > 0 MeV. In order to explain this discrepancy at low T, a new formalism has been put forward by including GDR induced quadrupole moment in the TSFM.     

Thermal birefringence-compensated linear intracavity frequency doubled Nd:YAG rod laser with 73 ns pulse duration and 160 W green output power

In a thermally birefringence-compensated linear cavity configuration, ～160 W of average green power by intracavity frequency doubling of AO Q-switched Nd:YAG/LBO-based laser is demonstrated. The corresponding optical to optical conversion efficiency is estimated to be ～ 12.7%. The pulse repetition rate is 20 kHz with the individual pulse duration of 73 ns. The beam quality parameter is measured to be 18.     

Quantum Jarzynski equality with multiple measurement and feedback for isolated system

In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast with the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.