J. Magnan

Florida State University | FSU · Department of Mathematics

Lung cancer has the highest mortality rate of all cancers in both men and women. The algorithmic detection, characterization, and diagnosis of abnormalities found in chest CT scan images can potentially aid radiologists by providing additional medical information to consider in their assessment. Lung nodule segmentation, i.e., the algorithmic delin...

We analyze the dynamics of the Poincaré map associated with the center manifold equations of double-diffusive thermosolutal convection near a codimension-four bifurcation point when the values of the thermal and solute Rayleigh numbers, RT and RS, are comparable. We find that the bifurcation sequence of the Poincaré map is analogous to that of the...

Using a perturbation method, we solve asymptotically the nonlinear partial differential equations that govern double-diffusive convection (with heat and solute diffusing) in a two-dimensional rectangular domain near a critical point in parameter space where the linearized operator has a quadruple-zero eigenvalue. The asymptotic solution near this c...

In the assessment of nodules in CT scans of the lungs, a number of image-derived features are diagnostically relevant. Currently, many of these features are defined only qualitatively, so they are difficult to quantify from first principles. Nevertheless, these features (through their qualitative definitions and interpretations thereof) are often q...

Genetic Algorithm optimization of sparse array parameters has been used to produce an ultrasonic beam with a higher, narrower main-lobe and lower side-lobes. The solutions obtained are neither unique nor trivial.

A wind-driven numerical model of the Indian Ocean is used to examine the horizontal statistics of hundreds of passive tracers spread evenly over the model domain. The distribution covers several dynamically distinct regions, revealing a variety of Lagrangian behaviours associated with different geographic locations. In particular, a cluster of traj...

We employ a MACSYMA program for the formal, perturbation, multiple bifurcation analysis of a system of nonlinear PDEs arising in double-diffusive convection. The program requires, as input, the system of PDEs to be solved, the form of the asymptotic expansion of the solution and of the bifurcation parameter, the solution of the adjoint linearized s...

The effects of rotation on secondary transitions of thermal convection in an infinite layer with finite Prandtl number and rigid boundaries are investigated analytically, expanding on the numerical results of Clever and Busse (1979). An asymptotic approach is employed to study the secondary transitions, to determine the secondary states, and to eva...

We consider the Boussinesq theory for convection in a rectangular box with imposed constant, negative, vertical heat and salt gradients. We analyze the bifurcation of two-dimensional convection steady states near a double instability point defined by a critical value of the thermal Rayleigh number and geometrical aspect ratio. We find that for ther...

Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of lambda-bifurcation and a generalization of it. lambda-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch o...

A perturbation analysis conceived for thermal convection states in a rotating box with a uniform temperature distribution on the walls is extended to the effect of a slightly nonuniform temperature distribution on a wall of the box, qualitatively altering the response of the convection system. This two-parameter study establishes that the vertical...

DOI:https://doi.org/10.1103/PhysRevA.32.1909

We analyze convection in a rectangular box where two ``substances,'' such as temperature and a solute, are diffusing. The solutions of the Boussinesq theory depend on the thermal and solute Rayleigh numbers RT and Rs, respectively, in addition to other geometrical and fluid parameters. As RT is increased, the conduction state becomes linearly unsta...

In this paper, we consider the mean-field equations for the laser with a saturable absorber (LSA) and concentrate on the low-intensity solutions. We show that the LSA equations may admit two successive bifurcations. The first bifurcation corresponds to the transition from the zero-intensity state to time-periodic intensities and is a Hopf bifurcati...

A cylindrical, weakly ionized and collision dominated neon plasma can be described by a system of nonlinear, parabolic reaction-diffusion equations for the electron and metastable atom axial densities. The equations exhibit a bifurcation from a uniform to a striated state at a critical length of the plasma column. The sharp transition between state...

by A.D. Kirwan Abstract. A wind-driven numerical model of the In- dian Ocean is used to examine the horizontal statistics of hundreds of passive

This paper consider the secondary and cascading bifurcation of two-dimensional steady and period thermal convection states in a rotating box. Previously developed asymptotic and perturbation methods that rely on the coalescence of two, steady convection, primary bifurcation points of the conduction state as the Taylor number approaches a critical v...