Uniform Spheroids Research Articles

Numerical evolution of radiative Robinson–Trautman spacetimes

The evolution of spheroids of matter emitting gravitational waves and a null radiation field is studied in the realm of radiative Robinson–Trautman spacetimes. The null radiation field is expected in realistic gravitational collapse and can be either an incoherent superposition of waves of electromagnetic, neutrino or massless scalar fields. We have constructed the initial data identified as representing the exterior spacetime of uniform and non-uniform spheroids of matter. By imposing that the radiation field is a decreasing function of the retarded time, the Schwarzschild solution is the asymptotic configuration after an intermediate Vaidya phase. The main consequence of the joint emission of gravitational waves and the null radiation field is the enhancement of the amplitude of the emitted gravitational waves. Another important issue we have touched on is the mass extraction of the bounded configuration through the emission of both types of radiation.

Micropatterned organoid culture of rat hepatocytes and HepG2 cells

The culture of liver cell organoids (multicellular aggregates) such as spheroids or cylindroids, which can strongly express liver functions, has been advocated as a useful technique that has advantages over monolayer culture. This paper describes a micropatterning technique for obtaining spheroids and cylindroids by using rat hepatocytes or HepG2 cells. We developed culture chips that comprised multiple, circular or rectangular microwells; the bottom surface of each microwell was modified with collagen to create a cell adhesion area, and the entire microwell, excluding the collagen-coated spots, was modified with polyethylene glycol (PEG) to create a nonadhesive area. Rat hepatocytes and HepG2 cells formed uniform spheroids and cylindroids on the circular and rectangular chips, respectively. Consequently, two-dimensional micropatterned chips containing homogeneous spheroids or cylindroids were generated. The expression of liver functions (protein secretion and ammonia removal) was greater in the spheroids and cylindroids than in the monolayer culture, and this expression was maintained for at least 2 weeks of culture. Thus, this chip technology has potential for use in various applications that involve organoid culture.

Scaffold-Free Three-Dimensional Cell Culture Utilizing Micromolded Nonadhesive Hydrogels

Techniques that allow cells to self-assemble into three-dimensional (3-D) spheroid microtissues provide powerful in vitro models that are becoming increasingly popular--especially in fields such as stem cell research, tissue engineering, and cancer biology. Unfortunately, caveats involving scale, expense, geometry, and practicality have hindered the widespread adoption of these techniques. We present an easy-to-use, inexpensive, and scalable technology for production of complex-shaped, 3-D microtissues. Various primary cells and immortal cell lines were utilized to demonstrate that this technique is applicable to many cell types and highlight differences in their self-assembly phenomena. When seeded onto micromolded, nonadhesive agarose gels, cells settle into recesses, the architectures of which optimize the requisite cell-to-cell interactions for spontaneous self-assembly. With one pipeting step, we were able to create hundreds of uniform spheroids whose size was determined by seeding density. Multicellular tumor spheroids (MCTS) were assembled or grown from single cells, and their proliferation was quantified using a modified 4-[3-(4-iodophenyl)-2-(4-nitrophenyl)-2H-5-tetrazolio]-1,3-benzene disulfonate (WST-1) assay. Complex-shaped (e.g., honeycomb) microtissues of homogeneous or mixed cell populations can be easily produced, opening new possibilities for 3-D tissue culture.

Technique for the control of spheroid diameter using microfabricated chips

This paper describes a new technique for the control of spheroid diameter in liver-derived cell lines using microfabricated chips that were prepared by combining microfabrication with chemical surface modification. The chip possesses multicavities in a triangular arrangement in the central region (10 mm × 10 mm) of a polymethylmethacrylate (PMMA) plate (24 mm × 24 mm), and the surface of the chip was modified with polyethylene glycol, thereby producing a surface that is non-adhesive to cells. HepG2 cells, a model liver-derived cell line, inoculated onto the chip were trapped within each cavity and proliferated to gradually form spheroids with smooth surfaces and high circularity. Although the spheroid diameters increased with cell proliferation during the initial 10 days of culture, they remained constant thereafter. The spheroid diameters were dependent on the scales of the multicavities on the chip, and the spheroid configuration with uniform diameter was maintained for at least 1 month. In particular, it was demonstrated using chips of various designs that the cavity diameter and the pitch between cavities were effective factors in controlling the spheroid diameter. Furthermore, the protein secretion activities of the spheroid formed on the chip were higher than those of the monolayers for at least 1 month of culture. These results indicate that this chip is a useful technique for the control of spheroid diameter and for the mass preparation of uniform spheroids.

Cover Picture: Shaping Mesoporous Silica Nanoparticles by Disassembly of Hierarchically Porous Structures (Angew. Chem. Int. Ed. 11/2007)

Colloidal crystals assembled from monodisperse spherical particles, have been used to template macroporous replicas with an inverse opal structure. Stein and co‐workers describe in their Communication on page 1885 ff. that uniform mesoporous silica cubes, tetrapods, and spheroids are produced by controlled disassembly of inverse opal silica samples. The shaped nanoparticles can be replicated into carbon or polymer shapes by nanocasting techniques.

Applicability of quasi-static and Rayleigh approximations for spheroidal particles

Expressions are obtained for the efficiency of absorption and scattering of radiation by uniform spheroids in the quasi-static approximation and the region of their applicability is studied. The prolate and oblate nonabsorbing particles with refractive indices 1.1≤n≤10 and axial ratios 1.1≤a/b≤100 were studied. The approximation expressions are found for the particle size at which the efficiency factors are calculated in the quasi-static approximation with an accuracy of 1%.

Relaxation of Star Clusters and Color Gradients

Large interstellar distances imply that protostars are dynamically decoupled from gas ram pressure (see, e.g., Aarseth, Lin & Papaloizou 1988) and are effectively isolated self-gravitating objects. With this in mind we apply Newtonian gravity to collapsing cold spheroids of point masses to model the Lin-Mestel-Shu (1965) solution for dust. Incomplete violent relaxation (e.g., van Albada 1982) means that traces of the initial orbit distribution in energy remain. We show here that furthermore the degree of orbit mixing achieved correlates well with initial morphology, by collapsing two-mass component uniform spheroids of different aspect ratio. We setup a test problem to seek out a relation between orbit survival and initial morphology which we then solve numerically.

Undamped oscillations of collisionless stellar systems: Spheres, spheroids and discs

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed

Synthesis of Monodispersed Zirconia Fine Particles

1) Submicron monodispersed ZrO2 fine particles were synthesized by the hydrolysis of Zr(nOBu)4 in n-propanol.2) The particles were uniform spheroids ranging in size from 0.4 to 0.8μm and free from agglomeration. X-ray and DTA-TG analysis showed particles were amorphous and hydrated.

Anisotropic explosion of rotating, self-gravitating uniform spheroids

The explosion of a uniformly rotating, spatially homogeneous spheroid with an internal pressure is followed numerically for various initial conditions and for different pressure-density relations. One particularly intriguing result is that very prolate (about the axis of rotation) configurations may be produced asymptotically for moderate energy release (i.e., slightly larger than the gravitational binding energy) whenever the explosion is not radiation dominated. We discuss briefly the relevance of our results in various astrophysical contexts like radio galaxies, supernovae, etc.

Analysis of the flexural vibrations of variable density spheroids immersed in an ideal fluid, with application to ship structural dynamics

An analysis is given of the characteristic flexural modes and frequencies of a linearly elastic free-free spheroid in an ideal fluid. The finite element method is used to represent the structural properties of a slender spheroid, employing a special element formulated for this purpose on the basis of Euler-Bernoulli beam theory. A consistent added mass matrix is derived from the exact solution of the infinite fluid potential problem, truncated at a suitable number of terms. A consistent added stiffness matrix is obtained for the buoyancy forces on a spheroid floating with its axis in a free surface, but other free surface effects (associated with wave generation) are assumed negligible. Solutions are computed for different aspect-ratio variable density spheroids vacuo , deeply submerged, and floating. The results indicate the possibility of considerable distortions in the lowest (‘rigid’) modes of slender floating bodies vibrating in a vertical plane, and illustrate the difficulty of defining three dimensional reduction factors for use with a simplified two dimensional theory. Derivation of the classical reduction factors for uniform density spheroids is given by way of comparison. The paper provides an illustration of use of a finite element formulation, in conjunction with consistent added mass and stiffness matrices, for a rational analysis of the structural dynamics of ships and other marine vehicles.

Morphologic changes in gelled synthetic latices

A photomicrographic study was made of the transformations undergone by synthetic latices during concentration by a method involving electrolyte addition, gelation, cooling and subsequent filtration. This investigation has disclosed that in latex-salt mixes suitably adjusted and processed for concentration a characteristic structure is present consisting of quite uniform spheroids suspended in a medium of clear serum. This spheroidal structure has been found to be essential for filterability, the rate of filtration being the faster the larger and more uniform the spheroids. During filtration only serum is removed, the spheroids remaining as a residue. On warming the filter residue the spheroidal particles disintegrate to give again a latex free of coagulum. Photomicrographic study has shown that the spheroids consist of small particles of apparently polymer, embedded in a transparent matrix of presumably soap gel. When the spheroids are warmed the gel breaks down, and the particles diffuse into and are dispersed in the surrounding medium. These phenomena indicate that the spheroids are temporary low temperature agglomerates of rubber and soap which disintegrate into finer latex particles as soon as the temperature is raised above a critical point. The stability of the spheroids is dependent principally upon electrolyte content, temperature and the amount and type of emulsifier present. The above structure has been found in processed and filterable Type II, Type III, GR-S 10, Buna S-3, Hyear OR, and “cold rubber” latex-electrolyte mixes.