PART 1 DEALS WITH THE DYNAMIC ASPECTS OF THE SUBJECT: MATHEMATICAL ANALYSIS OF SYSTEMS SUBJECTED TO INDEPENDENT VIBRATIONS BY MEANS OF MATHEMATICAL MODELS. THE ANALYTICAL SYSTEMS USED ARE NON-LINEAR SYSTEMS, HYDRODYNAMICS AND NUMERICAL METHODS. PART 2 EXAMINES SEISMIC MOVEMENTS, THE DYNAMIC BEHAVIOUR OF STRUCTURES AND THE BASIC CONCEPTS OF THE SEISMIC DESIGN OF STRUCTURES.

Fundamentals of earthquake engineering

The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

From the NJIT Department of Civil and Environmental Engineering, the Graduate Certificate in Environmental Engineering allows students to focus in Water Quality, Treatment and Infrastructure, Integrated Site Remediation, or Multidisciplinary Environmental Engineering. Environmental Engineers are interested in ways to protect the environment, improve water quality, and are essential in planning, designing and constructing water and wastewater treatment plants, solid waste disposal systems, site remediation approaches and emission control measures.

Environmental engineering-i

Review of theory of distortion and disintegration of liquid streams

This work is motivated by the recent experimental development of microfluidic flow-focusing devices that produce highly monodisperse simple or compound drops. Using finite elements with adaptive meshing in a diffuse-interface framework, we simulate the breakup of simple and compound jets in coflowing conditions, and explore the flow regimes that prevail in different parameter ranges. Moreover, we investigate the effects of viscoelasticity on interface rupture and drop pinch-off. The formation of simple drops exhibits a dripping regime at relatively low flow rates and a jetting regime at higher flow rates. In both regimes, drops form because of the combined effects of capillary instability and viscous drag. The drop size increases with the flow rate of the inner fluid and decreases with that of the outer fluid. Viscoelasticity in the drop phase increases the drop size in the dripping regime but decreases it in the jetting regime. The formation of compound drops is a delicate process that takes place in a narrow window of flow and rheological parameters. Encapsulation of the inner drop depends critically on coordination of capillary waves on the inner and outer interfaces.

Formation of simple and compound drops in microfluidic devices

The newly developed critical angle refractometry and sizing technique (CARS) allows simultaneous and instantaneous characterization of the local size distribution and the relative refractive index (i.e. composition) of a cloud of bubbles. The paper presents the recent improvement of this technique by comparison of different light scattering models and inversion procedures. Experimental results carried in various air/water and air/water-ethanol bubbly flows clearly demonstrate the efficiency and the potential of this technique.

Optical characterization of bubbly flows with a near-critical-angle scattering technique

The freezing of a supercooled droplet occurs in two steps: recalescence, that is, a rapid return to thermodynamic equilibrium at the freezing temperature leading to a liquid–solid mixture and a longer stage of complete freezing. The second freezing step can be modelled by the one-phase Stefan problem for an inward solidification of a sphere, assuming the droplet to be spherical. A convective heat transfer with the ambient immiscible fluid is modelled by a mixed boundary condition on the outer surface of the droplet. This condition depends on the Biot number (ratio of the heat transfer resistances inside the droplet and at its surface). A novel asymptotic solution is developed for a small Stefan number and an arbitrary Biot number. Applying the method of matched asymptotic expansions, uniformly valid solutions are obtained for the temperature profile and freezing front evolution in the whole stage of complete freezing. For an infinite Biot number, that is, for a fixed temperature at the droplet outer boundary, known solutions are recovered. In parallel, numerical results are obtained for an arbitrary Stefan number using a finite-difference scheme based on the enthalpy method. The asymptotic and numerical solutions are in good agreement.

Freezing of a supercooled spherical droplet with mixed boundary conditions

Linear capillary instability of compound jets

This paper analyzes various phenomena in modeling the light-scattering properties of large spherical bubbles in the context of geometrical and physical optics approximations. Among these phenomena are interference occurring between higher-order rays, the Goos–Hanchen shift, the tunneling phase and the weak caustic associated with the critical angle. When the phenomena are appropriately taken into account, they allow retrieval of most features of the scattering diagrams predicted by the Lorenz–Mie theory, offering new possibilities for the optical characterization of bubbly flows.

Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations

A first-order approximation is derived for the near-critical-angle scattering of a large spheroidal bubble illuminated by a plane wave propagating along the bubble axis of symmetry. The intensity of the far-field scattering pattern is expressed as a function of the relative refractive index and the two radii of curvature of the spheroidal bubble at the critical impact point.

Stefan Radev

Papers

Optical characterization of bubbly flows with a near-critical-angle scattering technique

Freezing of a supercooled spherical droplet with mixed boundary conditions

Linear capillary instability of compound jets

Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations

Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles.