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Implementation of Parallel Computing Technology to Vortex Flow

Mainframe supercomputers such as the Cray C90 was invaluable in obtaining large scale computations using several millions of grid points to resolve salient features of a tip vortex flow over a lifting wing. However, real flight configurations require tracking not only of the flow over several lifting wings but its growth and decay in the near- and intermediate- wake regions, not to mention the interaction of these vortices with each other. Resolving and tracking the evolution and interaction of these vortices shed from complex bodies is computationally intensive. Parallel computing technology is an attractive option in solving these flows. In planetary science vortical flows are also important in studying how planets and protoplanets form when cosmic dust and gases become gravitationally unstable and eventually form planets or protoplanets. The current paradigm for the formation of planetary systems maintains that the planets accreted from the nebula of gas and dust left over from the formation of the Sun. Traditional theory also indicate that such a preplanetary nebula took the form of flattened disk. The coagulation of dust led to the settling of aggregates toward the midplane of the disk, where they grew further into asteroid-like planetesimals. Some of the issues still remaining in this process are the onset of gravitational instability, the role of turbulence in the damping of particles and radial effects. In this study the focus will be with the role of turbulence and the radial effects.

Dacles-Mariani, Jennifer↗

Microphysical Processes Affecting the Pinatubo Volcanic Plume

In this paper we consider microphysical processes which affect the formation of sulfate particles and their size distribution in a dispersing cloud. A model for the dispersion of the Mt. Pinatubo volcanic cloud is described. We then consider a single point in the dispersing cloud and study the effects of nucleation, condensation and coagulation on the time evolution of the particle size distribution at that point.

Hamill, Patrick↗

Global to Microscale Evolution of the Pinatubo Volcanic Aerosol Derived from Diverse Measurements and Analyses

We assemble data on the Pinatubo aerosol from space, air, and ground measurements, develop a composite picture, and assess the consistency and uncertainties of measurement and retrieval techniques. Satellite infrared spectroscopy, particle morphology, and evaporation temperature measurements agree with theoretical calculations in showing a dominant composition of H2SO4-H20 mixture, with H2SO4 weight fraction of 65-80% for most stratospheric temperatures and humidities. Important exceptions are (1) volcanic ash, present at all heights initially and just above the tropopause until at least March 1992, and (2) much smaller H2SO4 fractions at the low temperatures of high-latitude winters and the tropical tropopause. Laboratory spectroscopy and calculations yield wavelength- and temperature-dependent refractive indices for the H2SO4-H20 droplets. These permit derivation of particle size information from measured optical depth spectra, for comparison to impactor and optical-counter measurements. All three techniques paint a generally consistent picture of the evolution of R(sub eff), the effective radius. In the first month after the eruption, although particle numbers increased greatly, R(sub eff) outside the tropical core was similar to preeruption values of approx. 0.1 to 0.2 microns, because numbers of both small (r < 0.2 microns) and large (r > 0.6 microns) particles increased. In the next 3-6 months, extracore R(sub eff) increased to approx. 0.5 microns, reflecting particle growth through condensation and coagulation. Most data show that R(sub eff) continued to increase for about 1 year after the eruption. R(sub eff) values up to 0.6 - 0.8 microns or more are consistent with 0.38 - 1 micron optical depth spectra in middle to late 1992 and even later. However, in this period, values from in situ measurements are somewhat less. The difference might reflect in situ undersampling of the very few largest particles, insensitivity of optical depth spectra to the smallest particles, or the inability of flat spectra to place an upper limit on particle size. Optical depth spectra extending to wavelengths lambda > 1 micron are required to better constrain R(sub eff), especially for R(sub eff) > 0.4 microns. Extinction spectra computed from in situ size distributions are consistent with optical depth measurements; both show initial spectra with lambda(sub max) <= 0.42 microns, thereafter increasing to 0.78 <= lambda(sub max) <= 1 micron. Not until 1993 do spectra begin to show a clear return to the preeruption signature of lambda(sub max) <= 0.42 microns. The twin signatures of large R(sub eff) (> 0.3 microns) and relatively flat extinction spectra (0.4 - 1 microns) are among the longest-lived indicators of Pinatubo volcanic influence. They persist for years after the peaks in number, mass, surface area, and optical depth at all wavelengths <= 1 microns. This coupled evolution in particle size distribution and optical depth spectra helps explain the relationship between global maps of 0.5- and 1.0-micron optical depth derived from the Advanced Very High Resolution Radiometer (AVHRR) and Stratospheric Aerosol and Gas Experiment (SAGE) satellite sensors. However, there are important differences between the AVHRR and SAGE midvisible optical thickness products. We discuss possible reasons for these differences and how they might be resolved.

Russell, P. B.↗

Metal Nanoparticle Aerogel Composites

We have fabricated sol-gels containing gold and silver nanoparticles. Formation of an aerogel produces a blue shift in the surface plasmon resonance as a result of the decrease in the dielectric constant of the matrix upon supercritical extraction of the solvent. However, as a result of chemical interface damping this blue shift does not obey effective medium theories. Annealing the samples in a reducing atmosphere at 400 C eliminates this discrepancy and results in narrowing and further blue shifting of the plasmon resonance. Metal particle aggregation also results in a deviation from the predictions of effective medium theories, but can be controlled through careful handling and by avoiding the use of alcohol. By applying effective medium theories to the heterogeneous interlayer surrounding each metal particle, we extend the technique of immersion spectroscopy to inhomogeneous materials characterized by spatially dependent dielectric constants, such as aerogels. We demonstrate that the shift in the surface plasmon wavelength provides the average fractional composition of each component (air and silica) in this inhomogeneous layer, i.e. the porosity of the aerogel or equivalently, for these materials, the catalytic dispersion. Additionally, the kinetics suggest that collective particle interactions in coagulated metal clusters are perturbed during silica gelation resulting in a change in the aggregate geometry.

Smith, David D.↗

Aerosol Modeling for the Global Model Initiative

The goal of this project is to develop an aerosol module to be used within the framework of the Global Modeling Initiative (GMI). The model development work will be preformed jointly by the University of Michigan and AER, using existing aerosol models at the two institutions as starting points. The GMI aerosol model will be tested, evaluated against observations, and then applied to assessment of the effects of aircraft sulfur emissions as needed by the NASA Subsonic Assessment in 2001. The work includes the following tasks: 1. Implementation of the sulfur cycle within GMI, including sources, sinks, and aqueous conversion of sulfur. Aerosol modules will be added as they are developed and the GMI schedule permits. 2. Addition of aerosol types other than sulfate particles, including dust, soot, organic carbon, and black carbon. 3. Development of new and more efficient parameterizations for treating sulfate aerosol nucleation, condensation, and coagulation among different particle sizes and types.

Weisenstein, Debra K.↗

The Effect of Microgravity on the Growth of Silica Nanostructures

The process of the formation of structures from coagulating ensembles is fundamentally important since the collective behavior of the constituents often results in dramatically improved or unusual mechanical, thermal, chemical, and optical properties. In this study we examine the effect of microgravity on the formation of silica structures, specifically particles and gels.

Smith, D. D.↗

Formation and Early Evolution of Solar and Extra-Solar Giant Planets

This project investigates the origin of giant planets, both in the Solar System and around other stars. It is assumed that the planets form by the core accretion process: small solid particles in a disk surrounding a young star gradually coagulate into objects of a few kilometers in size, known as planetesimals, which then accumulate into solid protoplanetary cores. Once the cores have become large enough, they are able to attract gas from the surrounding disk to form the deep gaseous envelope of the giant planet. Our code simulates giant planet growth in a spherical approximation, and it has been quite successful in addressing a number of basic planetary properties. Further improvements to the code have been made to achieve a more realistic understanding of planetary formation. The computations of the models were based on an earlier version of our code and were stopped at the onset of runaway gas accretion. Now, improved boundary conditions have been incorporated into the code to allow for hydrodynamic inflow of gas and to handle the late stages of evolution when the planet evolves at constant mass. These changes were made to the version of the code that uses a constant accretion rate and to the version that uses a self-consistent method for calculating both the solid and gas accretion rates. The equation of state has been updated to incorporate the detailed tables of Saumon, Chabrier, and Van Horn. The opacities were updated to include the results of Alexander and Ferguson. The outer boundary conditions were modified. During the accretion phase when the planet's radius is between the accretion radius and the tidal radius, we set the outer boundary at a 'modified' accretion radius, which is the point where thermal energy is enough to bring gas to the edge of the Hill sphere.

Bodenheimer, P. H.↗

Global Distribution and Sources of Volatile and Nonvolatile Aerosol In the Remote Troposphere

Airborne measurements of aerosol (Condensation Nuclei, CN) and selected trace gases made in the areas of the North Atlantic Ocean during SONEX (October/November 1997), and the south tropical Pacific Ocean during PEM-Tropics A (September/October 1996) and PEM-Tropics B (March/April 1999) have been analyzed. Emphasis is on the interpretations of variations in the number densities of the fine (>17 nm) and ultrafine (>8 nm) CN in the upper troposphere (8-12 km). These data suggest that large number densities of highly volatile CN (10(exp 4)-10(exp 5)/cu cm) are present in the clean upper troposphere with highest values over the tropical1subtropical region. Through marine convection and long-distance horizontal transport, volatile CN originating from the tropical/subtropical regions can frequently impact the abundance of aerosol in the middle and upper troposphere at mid to high latitudes. Nonvolatile aerosol particles behave in a manner similar to tracers of combustion (CO) and photochemical pollution (PAN), implying a source from continental pollution of industrial or biomass burning origin. In the upper troposphere, we find that volatile and nonvolatile partials number densities are inversely correlated. An aerosol microphysical model is used to suggest that coagulation of fine volatile particles with fewer larger nonvolatile particles provides one possible mechanism for this relationship. It appears that nonvolatile particles, of principally anthropogenic origin,provide a highly efficient removal process for the fine volatile aerosol.

Singh, Hanwant B.↗

Disintegration of Dust Aggregates in Interstellar Shocks and the Lifetime of Dust Grains in the ISM

Interstellar grains are destroyed by shock waves moving through the ISM. In fact, the destruction of grains may be so effective that it is difficult to explain the observed abundance of dust in the ISM as a steady state between input of grains from stellar sources and destruction of grains in shocks. This is especially a problem for the larger grains. Therefore, the dust grains must be protected in some way. Jones et al. have already considered coatings and the increased post-shock drag effects for low density grains. In molecular clouds and dense clouds, coagulation of grains is an important process, and the largest interstellar grains may indeed be aggregates of smaller grains rather than homogeneous particles. This may provide a means to protect the larger grains, in that, in moderate velocity grain-grain collisions in a shock the aggregates may disintegrate rather than be vaporized. The released small particles are more resilient to shock destruction (except in fast shocks) and may reform larger grains later, recovering the observed size distribution. We have developed a model for the binding forces in grain aggregates and apply this model to the collisions between an aggregate and fast small grains. We discuss the results in the light of statistical collision probabilities and grain life times.

Dominik, C.↗

Aerosol Radiative Effects: Expected Variations in Optical Depth Spectra and Climate Forcing, with Implications for Closure Experiment Strategies

We examine measurement strategies for reducing uncertainties in aerosol direct radiative forcing by focused experiments that combine surface, air, and space measurements. Particularly emphasized are closure experiments, which test the degree of agreement among different measurements and calculations of aerosol properties and radiative effects. By combining results from previous measurements of large-scale smokes, volcanic aerosols, and anthropogenic aerosols with models of aerosol evolution, we estimate the spatial and temporal variability in optical depth spectra to be expected in the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX, planned for summer 1996 off the Eastern U.S. seaboard). In particular, we examine the expected changes in the wavelength dependence of optical depth as particles evolve through nucleation, growth by condensation and coagulation, and removal via sedimentation. We then calculate the expected radiative climate forcing (i.e. change in net radiative flux) for typical expected aerosols and measurement conditions (e.g. solar elevations, surface albedos, radiometer altitudes). These calculations use new expressions for flux and albedo changes, which account not only for aerosol absorption, but also for instantaneous solar elevation angles and the dependence of surface albedo on solar elevation. These factors, which are usually ignored or averaged in calculations of global aerosol effects, can have a strong influence on fluxes measured in closure experiments, and hence must be accounted for in calculations if closure is to be convincingly tested. We compare the expected measurement signal to measurement uncertainties expected for various techniques in various conditions. Thereby we derive recommendations for measurement strategies that combine surface, airborne, and spaceborne measurements.

Russell, Philip B.↗

Pinatubo Aerosol Global-to-Micro-Scale Evolution: A Unified Picture From Space, Air, and Ground Measurements

We combine a variety of measurements to develop a composite picture of the post-Pinatubo aerosol and assess the consistency and uncertainties of the measurement and retrieval techniques Satellite infrared spectroscopy, particle morphology, and evaporation temperature measurements are in accord with theoretical calculations In showing a dominant particle composition of H2SO4-H2O mature with H2SO4 weight traction of 65-80% for most stratospheric temperatures and humidities. Important exceptions are: (1) the presence of volcanic ash at all attitudes initially and in a layer just above the tropopause until at least March 1992, and (2) much smaller H2SO4 weight fractions at the low temperatures attained In high latitude winters and at the tropical tropopause. Laboratory spectroscopy and theoretical calculations yield wavelength- and temperature-dependent refractive indices for the dominant H2SO4-H2O droplets. These in turn permit derivation of particle size spectra from measured optical depth spectra for comparison to direct measurements by impactors and optical counters, All three techniques paint a generally consistent picture of the evolution of R(sub eff) the effective, or area-weighted, particle radius. In the first month after the eruption, although particle numbers increased by orders of magnitude, R(sub eff) was similar to the pre-eruption value of 0.1 to 0.2 microns because both small (r less than 0.2 microns) and large (r greater than 0.6 microns) particles increased in number. Over the next 3-6 months, R(sub eff) increased to about 0.5 microns, reflecting particle growth through condensation and coagulation. In general, R(sub eff) continued to increase for about a year after the eruption. Extinction spectra computed from in situ size distribution measurements are consistent with optical depth measurements, which show spectra with maxima initially at wavelengths of 0.42 microns or less, and thereafter progressively increasing to between 0.78 and 1 micron. Not until 1993 does optical depth spectra begin to show a clear return to the preeruption signature of maximizing at the shortest visible wavelengths or in the near UV. This coupled evolution in particle size distribution and optical depth spectra helps explain the relationship between the global maps of 0.5- and 1.0-kilometer optical depth derived from the AVHRR and SAGE satellite measurements. It also sets a context for evaluating remaining uncertainties in each of these satellite data products. We also show how the effects of wavelength-dependent refractive index on backscatter spectra can influence particle sizes retrieved from multiwavelength lidar measurements.

Russell, Philip B.↗

A Unified Picture of Pinatubo Aerosol Global-to Micro-Scale Evolution, From Space, Air, and Ground Measurements

We combine a variety of measurements to develop a composite picture of the post-Pinatubo aerosol and assess the consistency and uncertainties of the measurement and retrieval techniques. Satellite infrared spectroscopy, particle morphology, and evaporation temperature measurements are in accord with theoretical calculations in showing a dominant particle composition of H2SO4-H2O mixture, with H2SO4 weight fraction of 65-80% for most stratospheric temperatures and humidities. Important exceptions are: (1) the presence of volcanic ash at all altitudes initially and in a layer just above the tropopause until at least March 1992, and (2) much smaller H2SO4 weight fractions at the low temperatures attained in high latitude winters and at the tropical tropopause, Laboratory spectroscopy and theoretical calculations yield wavelength- and temperature-dependent refractive indices for the dominant H2SO4-H2O droplets. These in turn permit derivation of particle size spectra from measured optical depth spectra, for comparison to direct measurements by impactors and optical counters. All three techniques paint a generally consistent picture of the evolution of R(sub eff), the effective, or area-weighted, particle radius. In the first month after the eruption, although particle numbers increased by orders of magnitude, R(sub eff) was similar to the preemption value of 0.1 to 0.2 microns, because both small (r less than 0.2 microns) and large (r greater than 0.6 micron particles increased in number. Over the next 3-6 months, R(sub eff) increased to about 0.5 microns reflecting particle growth through condensation and coagulation. In general, R(sub eff) continued to increase for about a year after the eruption. Extinction spectra computed from in situ size distribution measurements are consistent with optical depth measurements, which show spectra with maxima initially at wavelengths of 0.42 microns or less, and thereafter progressively increasing to between 0.78 and 1 micron. Not until 1993 do optical depth spectra begin to show a clear return to the preemption signature of maximizing at the shortest visible wavelengths or in the near UV. This coupled evolution in particle size distribution and optical depth spectra helps explain the relationship between the global maps of 0.5- 1.0- micron optical depth derived from the AVHRR and SAGE satellite measurements.

Russell, Philip B.↗

H2, CO and Dust Emission Around Low Mass Stars

We model the thermal balance, the chemistry, and the radiative transfer in dusty disks orbiting young, low mass stars. These models are motivated by observations of infrared and ultraviolet transitions of H2 from protoplanetary disks, as well as millimeter and submillimeter observations of other molecules such as CO, and infrared continuum observations of the dust. The dust grains are heated primarily by the stellar radiation and the infrared radiation field produced by the dust itself. The gas is heated by collisions with warmer dust grains, X-rays from the region close to the stellar surface, UV pumping of hydrogen molecules, and the grain photoelectric heating mechanism initiated by UV photons from the central star. We treat cases where the gas to dust ratio is high, because the dust has settled to the midplane and coagulated into relatively large objects. We discuss situations in which the infrared emission from H2 can be detected, and how the comparison of the observations with our models can deduce physical parameters such as the mass and the density and temperature distribution of the gas.

Hollenbach, David↗

Magnetic Microspheres for Therapeutical Applications

Hyperthermia is a well known cancer therapy and consists of heating a tumor region to the elevated temperatures in the range of 40-45 C for an extended period of time (2-8 hours). This leads to thermal inactivation of cell regulatory and growth processes with resulting widespread necrosis, carbonization and coagulation. Moreover, heat boosts the tumor response to other treatments such as radiation, chemotherapy or immunotherapy. Of particular importance is careful control of generated heat in the treated region and keeping it localized. Higher heating, to about 56 C can lead to tissue thermo-ablation. With accurate temperature control, hyperthermia has the advantage of having minimal side effects. Several heating techniques are utilized for this purpose, such as whole body hyperthermia, radio-frequency (RF) hyperthermia, ultrasound technique, inductive microwave antenna hyperthermia, inductive needles (thermoseeds), and magnetic fluid hyperthermia (MFH).MFH offers many advantages as targeting capability by applying magnets. However, this technology still suffers significant inefficiencies due to lack of thermal control. This paper will provide a review of the topic and outline the ongoing work in this area. The main emphasis is in devising ways to overcome the technical difficulty in hyperthermia therapy of achieving a uniform therapeutic temperature over the required region of the body and holding it steady. The basic obstacle of the present heating methods are non-uniform thermal properties of the tissue. Our approach is to develop a novel class of magnetic fluids which have inherent thermoregulating properties. We have identified a few magnetic alloys which can serve as a suitable nano-particle material. The objective is to synthesize, characterize and evaluate the efficacy of TRMF for hyperthermia therapy.

Mazuruk, K.↗

H2, CO and Dust Emission Around Low Mass Stars

We model the thermal balance, the chemistry, and the radiative transfer in dusty disks orbiting young, low mass stars. These models are motivated by observations of infrared and ultraviolet transitions of H2 from protoplanetary disks, as well as millimeter and submillimeter observations of other molecules such as CO, and infrared continuum observations of the dust. The dust grains are heated primarily by the stellar radiation and the infrared radiation field produced by the dust itself. The gas is heated by collisions with warmer dust grains, X-rays from the region close to the stellar surface, UV (ultraviolet) pumping of hydrogen molecules, and the grain photoelectric heating mechanism initiated by UV photons from the central star. We treat cases where the gas to dust ratio is high, because the dust has settled to the midplane and coagulated into relatively large objects. We discuss situations in which the infrared emission from H2 can be detected, and how the comparison of the observations with our models can deduce physical parameters such as the mass and the density and temperature distribution of the gas.

Hollenbach, David↗

Mixing and Transport in the Solar Nebula

Boss & Vanhala (2000, 2001) prepared reviews of triggered collapse and injection models, using Prudence Foster's finite differences code at very high spatial resolution (440 x 1440 cells) to demonstrate the convergence of the R-T fingers in triggered injection models. A two dimensional hydrodynamical calculation with unprecedentedly high spatial resolution (960 x 2880 zones, or almost 3 million grid points) demonstrated that it suitable shock front can both trigger the collapse of an otherwise stable presolar cloud, and inject shock front particles into the collapsing cloud through the formation of what become Rayleigh-Taylor fingers of compressed fluid layers falling into the gravitational potential well of the growing protostar. These calculations suggest that heterogeneity derived from these R-T fingers will persist down to the scale of their injection onto the surface of the solar nebula. Haghighipour developed a numerical code capable of calculating the orbital evolution of dust grains of varied sizes in a gaseous nebula, subject to Epstein and Stokes drag as well as the self-gravity of the disk. In collaboration with the PI and George W. Wetherill, Haghighipour has been involved in development of a new idea on the possibility of rapid formation of ice giant planets via the disk instability mechanism. Haghighipour studied the stability of a five-body system consisting of the Sun and four protoplanets by numerically integrating their equations of motions. Using Levison and Duncan s SWIFT integrator, Haghighipour showed that, depending on the orbital parameters of the bodies, such a system can be stable for 0.1-10 Myr. Time periods of 1 Myr or more are long enough to be consistent with the time scale proposed for the formation of giant planets by the disk instability mechanism and the photoevaporation of the gaseous envelopes of the outermost protoplanets by a nearby OB star, resulting in the formation of ice giant planets. The PI has used his three dimensional models of marginally gravitationally unstable disks to study the preservation of isotopic heterogeneity in evolving protoplanetary disks. Such heterogeneity might arise from the infall onto the disk s surface of solids processed in the X-wind region of the disk, or derived from stellar nucleosynthesis and injected by R-T fingers. The technique used consists of solving a color equation, identical to the gas continuity equation, which follows the time evolution in three space dimensions of an arbitrarily placed initial color field, i.e., a dye inserted the disk. The models show that significant concentrations of color could persist for time periods of about a thousand years or more, even in the most dynamically active region of such a disk. Such a time period might be long enough for solids to coagulate and grow to significant sizes while retaining the isotopic signature of their birth region in the nebula.

Boss, Alan P.↗

Entrainment and Optical Properties of an Elevated Forest Fire Plume Transported into the Planetary Boundary Layer near Washington, D.C.

Smoke and pollutants from Canadian forest fires were transported over the northeastern United States in July 2002. Lidar observations at the NASA Goddard Space Flight Center show the smoke from these fires arriving in an elevated plume that was subsequently transported to the surface. Trajectory and three-dimensional model calculations confirm the origin of the smoke and show that it mixed to the surface after it was intercepted by the turbulent planetary boundary layer. Modeled smoke optical properties agreed well with aircraft and remote sensing observations provided coagulation of smoke particles was accounted for in the model. Our results have important implications for the long-range transport of pollutants and their subsequent entrainment to the surface, as well as the evolving optical properties of smoke from boreal forest fires.

Colarco, P. R.↗

Magnetic Microspheres and Tissue Model Studies for Therapeutical Applications

Hyperthermia is a well known cancer therapy and consists of heating a tumor region to the elevated temperatures in the range of 40-45 C for an extended period of time (2-8 hours). This leads to thermal inactivation of cell regulatory and growth processes with resulting widespread necrosis, carbonization and coagulation. Moreover, heat boosts the tumor response to other treatments such as radiation, chemotherapy or immunotherapy. Of particular importance is careful control of generated heat in the treated region and keeping it localized. Higher heating, to about 56 C can lead to tissue thermo-ablation. With accurate temperature control, hyperthermia has the advantage of having minimal side effects. Several heating techniques are utilized for this purpose, such as whole body hyperthermia, radio-frequency (RF) hyperthermia, ultrasound technique, inductive microwave antenna hyperthermia, inductive needles (thermoseeds), and magnetic fluid hyperthermia (MFH).MFH offers many advantages as targeting capability by applying magnets. However, this technology still suffers significant inefficiencies due to lack of thermal control. This paper will provide a review of the topic and outline the ongoing work in this area. The main emphasis is in devising ways to overcome the technical difficulty in hyperthermia breast therapy of achieving a uniform therapeutic temperature over the required region of the body and holding it steady for an extended period (2-3 hours). The basic shortcomings of the presently utilized heating methods stem from the non-uniform thermal properties of the tissue and the point heating characteristics of the techniques without any thermal control. Our approach is to develop a novel class of magnetic fluids, which have inherent thermoregulating properties. We have identified a few magnetic alloys which can serve as suitable nano to micron-size particle material. The objective is to synthesize, characterize and evaluate the efficacy of Thermo Regulating Magnetic Fluids (TRMF) for hyperthermia therapy. The development of a tissue model and testing the fluid dynamics of particle motion, settling, distribution in the tissue matrix and heat generation will be discussed.

Ramachandran, N.↗