Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Seven retinal specializations in the tubular eye of the deep-sea pearleye, Scopelarchus michaelsarsi: A case study in visual optimization

The deep-sea pearleye, Scopelarchus michaelsarsi (Scopelarchidae) is a mesopelagic teleost with asymmetric or tubular eyes. The main retina subtends a large dorsal binocular field, while the accessory retina subtends a restricted monocular field of lateral visual space. Ocular specializations to increase the lateral visual field include an oblique pupil and a corneal lens pad. A detailed morphological and topographic study of the photoreceptors and retinal ganglion cells reveals seven specializations: a centronasal region of the main retina with ungrouped rod-like photoreceptors overlying a retinal tapetum; a region of high ganglion cell density (area centralis of 56.1x10(3) cells per mm(2)) in the centrolateral region of the main retina; a centrotemporal region of the main retina with grouped rod-like photoreceptors; a region (area giganto cellularis) of large (32.2+/-5.6 mu m(2)), alpha-like ganglion cells arranged in a regular array (nearest neighbour distance 53.5+/-9.3 mu m with a conformity ratio of 5.8) in the temporal main retina; an accessory retina with grouped rod-like photoreceptors; a nasotemporal band of a mixture of rod-and cone-like photoreceptors restricted to the ventral accessory retina; and a retinal diverticulum comprised of a ventral region of differentiated accessory retina located medial to the optic nerve head. Retrograde labelling from the optic nerve with DiI shows that approximately 14% of the cells in the ganglion cell layer of the main retina are displaced amacrine cells at 1.5 mm eccentricity. Cryosectioning of the tubular eye confirms Matthiessen's ratio (2.59), and calculations of the spatial resolving power suggests that the function of the area centralis (7.4 cycles per degree/8.1 minutes of are) and the cohort of temporal alpha-like ganglion cells (0.85 cycles per degree/70.6 minutes of are) in the main retina may be different. Low summation ratios in these various retinal zones suggests that each zone may mediate distinct visual tasks in a certain region of the visual field by optimizing sensitivity and/or resolving power.

Simulation and optimization of heated, inviscid flows in scramjet ducts

A space-marching code for the simulation and optimization of inviscid supersonic flow in three dimensions is described. The now in a scramjet module with a relatively complex three-dimensional geometry is examined and wall-pressure estimates are compared with experimental data. Given that viscous effects are not presently included, the comparison is reasonable. The thermodynamic compromise of adding heat in a diverging combustor is also examined. The code is then used to optimize the shape of a thrust surface for a simpler (box-section) scramjet module in the presence of uniform and nonuniform heat distributions. The optimum two-dimensional profiles for the thrust surface are obtained via a perturbation procedure that requires about 30-50 now solutions. It is found that the final shapes are fairly insensitive to the details of the heat distribution.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Decentralized control design for nonlinear plants: a v-metric approach

In this paper, a new v-metric based approach is proposed to design decentralized controllers for multi-unit nonlinear plants that admit a set of plant decompositions in an operating space. Similar to the gap metric approach in literature, it is shown that the operating space can also be divided into several subregions based on a v-metric indicator, and each of the subregions admits the same controller structure. A comparative case study is presented to display the advantages of proposed approach over the gap metric approach. (C) 2000 Elsevier Science Ltd. All rights reserved.

Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Genetic algorithms for continuous optimization problems - a concept of parameter-space size adjustment

The concept of parameter-space size adjustment is pn,posed in order to enable successful application of genetic algorithms to continuous optimization problems. Performance of genetic algorithms with six different combinations of selection and reproduction mechanisms, with and without parameter-space size adjustment, were severely tested on eleven multiminima test functions. An algorithm with the best performance was employed for the determination of the model parameters of the optical constants of Pt, Ni and Cr.

An optimization model for antibiotic use

There is a positive correlation between the intensity of use of a given antibiotic and the prevalence of resistant strains. The more you treat, more patients infected with resistant strains appears and, as a consequence, the higher the mortality due to the infection and the longer the hospitalization time. In contrast, the less you treat, the higher the mortality rates and the longer the hospitalization time of patients infected with sensitive strains that could be successfully treated. The hypothesis proposed in this paper is an attempt to solve such a conflict: there must be an optimum treatment intensity that minimizes both the additional mortality and hospitalization time due to the infection by both sensitive and resistant bacteria strains. In order to test this hypothesis we applied a simple mathematical model that allowed us to estimate the optimum proportion of patients to be treated in order to minimize the total number of deaths and hospitalization time due to the infection in a hospital setting. (C) 2007 Elsevier Inc. All rights reserved.