Shirish M. Chitanvis

Explosion of water droplets.

We use self-similarity to describe the motion of vapor emanating from a water droplet that has been exploded by a short pulse from a high energy laser. This approach allows us to obtain a qualitative description of the experiment of Kafalas and Herrmann.

Explosive vaporization of small droplets by a high-energy laser beam

We have constructed a model of the explosive vaporization of small droplets caused by the absorption of energy from a high‐energy laser beam. The model consists of polarizable fluid streaming from the exploded droplet and interacting with laser radiation. A novel criterion for the explosive vaporization in the droplet is introduced, in which the absorbed energy density has to be greater than the restrictive pressure due to surface tension. Self‐similarity is invoked to reduce the spherically symmetric problem involving hydrodynamics and Maxwell’s equations to simple quadrature. We have compared our model with experiments. An analytic solution has been obtained in a limiting case.

Simple approach to stimulated Brillouin scattering in glass aerosols

We have investigated the effects of stimulated Brillouin scattering on a transparent, spherical bead with a radius of the order of 25 μm, the wavelength of the incident laser being ~1 μm. We have used a simple approach with intuitive appeal that displays the fundamental physics. We consider two cases: (a) neither the pump field nor the Stokes field is on a Mie resonance of the spherical transparent bead; (b) both the pump field and the Stokes field are resonant. We derive explicit expressions for the electromagnetic differential scattering cross sections, using the Lippman–Schwinger equation for scalar electromagnetic field equations. Mie theory is utilized to estimate the occurrence of Mie resonances as the size parameter x = 2πa/λ is varied. We give quantitative estimates of the fraction of droplets expected to shatter owing to resonant stimulated Brillouin scattering in a polydisperse distribution.

A NONLINEAR QUASI-STATIC MODEL OF INTRACRANIAL ANEURYSMS

Biomathematical models of intracranial aneurysms can provide qualitative and quantitative information on stages of aneurysm development through elucidation of biophysical interactions and phenomena. However, most current aneurysm models, based on Laplaces law, are renditions of static, linearly elastic spheres. The primary goal of this study is to: 1. develop a nonlinear constitutive quasi-static model and 2. derive an expression for the critical size/pressure of an aneurysm, with subsequent applications to clinical data. A constitutive model of an aneurysm, based on experimental data of tissue specimens available in the literature, was incorporated into a time-dependent set of equations describing the dynamic behavior of a saccular aneurysm in response to pulsatile blood flow. The set of differential equations was solved numerically, yielding mathematical expressions for aneurysm radius and pressure. This model was applied to clinical data obtained from 24 patients presenting with ruptured aneurysms. Aneurysm development and eventual rupture exhibited an inverse relationship between aneurysm size and blood pressure. In general, the model revealed that rupture becomes highly probable for an aneurysm diameter greater than 2.0 mm and a systemic blood pressure greater than 125 mmHg. However, an interesting observation was that the critical pressure demonstrated a minimal sensitivity to the critical radius, substantiating similar clinical and experimental observations that blood pressure was not correlated, to any degree, with aneurysm rupture. Undulations in the aneurysm wall, presented by irregular multilobulated morphologies, could play an important role in aneurysm rupture. However, due to the large variation in results, more extensive studies will be necessary for further evaluation and validation of this model.

A continuum solvation theory of quadrupolar fluids

We have derived a generalization of Poisson’s equation, a fourth‐order partial differential equation, to describe the electrostatic behavior of polarizable, quadrupolar fluids. Our theory is in accord with the approach of Evangelista and Barbero. This equation was solved for the case of multipoles of arbitrary order placed at the center of a spherical cavity in a quadrupolar fluid. Our solution indicates that the quadrupolar portion of the disturbance created by an electrostatic probe in a polarizable quadrupolar fluid is localized to a distance of about a bohr, while asymptotically the fluid behaves as a polarizable medium. Internal field corrections as well as internal field gradient corrections have been computed. Fairly good agreement is found between our theory and the experimentally determined dielectric constant for carbon dioxide. The cavity model solution has been applied toward understanding the solvation of ions and dipolar molecules in supercritical carbon dioxide. We have used our theory to s...

Hemodynamic assessment of the development and rupture of intracranial aneurysms using computational simulations.

Intracranial aneurysms manifest themselves as sacculations within a weakened region of the vessel wall and pose substantial neurological risks upon rupture. A primary factor in the development and rupture stages of an aneurysm is hemodynamics and its degrading effects on the aneurysm wall. Wall dynamics and hemodynamics within a fully developed aneurysm were investigated using computational simulation techniques. To study wall dynamics, the aneurysm was modeled as a thing spherical shell with linearly elastic and plastic (viscoelastic) wall behavior. The sensitivity of this model to the biophysical parameters which describe it will assist in the quantitative assessment of factors predisposing to aneurysm rupture and subarachnoid hemorrhage. Flow dynamics simulations were performed for spherical aneurysms with rigid walls. We observed the development and motion of an annular vortex within the lateral sacculation. We also simulated a ruptured aneurysm by placing a tear near the neck of the aneurysm. Flow patterns showed blood flowing out during the initial stages of the flow, but displayed an inflow of blood soon thereafter, as the internal pressure dropped. These results are substantiated by the clinical observations that turbulent flow is observed within the aneurysm as evidenced by reduced bruits.

Effect of thermal blooming on pulse propagation through vaporizing aerosols

The effect of thermal blooming in the air is formulated within the framework of the radiative transfer equation. This is accomplished on the basis of the ray optics approach and the notion of an effective time-dependent absorption coefficient that describes the changes in the phase of the electric field caused by thermal blooming. In this approach, the beam spreading effects are entirely due to scattering from the aerosol cloud; the effect of vaporization of aerosols leads to a nonlinear coupling of the aerosols to radiation. The general setup is used to model numerically the propagation of a high energy laser beam through a cloud of aerosols distributed in the atmosphere. The limitations of the approach are outlined.

Aerosol clearing model for a high‐energy laser beam propagating through vaporizing media

We describe the clearing phenomenon that occurs when a continuous wave (cw) high‐energy laser beam, incident upon a cloud of hygroscopic droplets, vaporizes these droplets. We consider the case when the incident wavelength is greater than the average droplet radius. The model of F. A. Williams [Int. J. Heat Mass Transfer 8, 575 (1965)] is used to describe the vaporization of a single droplet. The propagation of the laser beam is described by the radiative transfer equation in one dimension. We establish the existence of an ‘‘inertial’’ characteristic time ti that it takes for evaporation to be established in an aerosol cloud. Agreement of our model with a set of experimental data on vaporizing fog is demonstrated.

Onset of self-assembly

We have formulated a theory of self-assembly based on the notion of local gauge invariance at the mesoscale. Local gauge invariance at the mesoscale generates the required long- range entropic forces responsible for self-assembly in binary systems. Our theory was applied to study the onset of mesostructure formation above a critical temperature in estane, a diblock copolymer. We used diagrammatic methods to transcend the Gaussian approximation and obtain a correlation length zeta ~ (c-c*)^-gamma, where c* is the minimum concentration below which self-assembly is impossible, c is the current concentration, and gamma was found numerically to be close to 2/3. The renormalized diffusion constant vanishes as the c* is approached, indicating the occurrence of critical slowing down, while the correlation function remains finite at the transition point.

Theory of polyelectrolytes in solvents

Using a continuum description, we account for fluctuations in the ionic solvent surrounding a Gaussian, charged chain and derive an effective short-ranged potential between the charges on the chain. This potential is repulsive at short separations and attractive at longer distances. The chemical potential can be derived from this potential. When the chemical potential is positive, it leads to a meltlike state. For a vanishingly low concentration of segments, this state exhibits scaling behavior for long chains. The Flory exponent characterizing the radius of gyration for long chains is calculated to be approximately 0.63, close to the classical value obtained for second order phase transitions. For short chains, the radius of gyration varies linearly with N, the chain length, and is sensitive to the parameters in the interaction potential. The linear dependence on the chain length N indicates a stiff behavior. The chemical potential associated with this interaction changes sign, when the screening length in the ionic solvent exceeds a critical value. This leads to condensation when the chemical potential is negative. In this state, it is shown using the mean-field approximation that spherical and toroidal condensed shapes can be obtained. The thickness of the toroidal polyelectrolyte is studied as a function of the parameters of the model, such as the ionic screening length. The predictions of this theory should be amenable to experimental verification.