Simple Spheres Research Articles

The kinetic theory of a simple, chemically reactive fluid: Scattering functions and relaxation processes

The purpose of this investigation is to develop a computationally tractable procedure for obtaining theoretical estimates of the correlation functions characteristic of a chemically reactive small-molecule fluid and for determining the spectral characteristics of the associated many-body modes. Generalized Enskog-type kinetic equations (appropriate both to low and high densities) are derived for fluid mixtures which include species capable of participating in bimolecular reactions such as AB+CD⇄AC+BD. The dynamics of the reactive events are treated according to the model of simple reactive spheres (SRS) and to a less restrictive, modified simple reactive sphere (MSRS) model, as well. The distribution functions of the various species are represented by bilinear expansions in terms of velocity basis functions and the associated expansion coefficients are identified with correlation functions of pairs of single-particle dynamical variables. The kinetic equations are then transformed into coupled sets of linear integrodifferential equations for these correlation functions. Finally, illustrative calculations are performed and results compared with available experimental data.

A simplified approach to molecular dynamics simulations of liquid crystals with atom–atom potentials

Molecular dynamics simulations have been performed for the nematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl (5CB) using a realistic atom–atom potential as well as a pseudorealistic atom–atom potential. The latter treats the phenyl rings in the 5CB molecule as simple spheres. This method allows a considerable decrease in computational time while still retaining important aspects of the structural anisotropy. Molecular ordering has been studied using both approaches by calculating order parameters for the principle molecular axis as well as for individual molecular segments. Molecular conformations and dynamics have been examined using dihedral angle distribution functions for the biphenyl core and for the alkyl chain. Analysis of the data allows the inter and intra molecular contributions to the conformational equilibria of the chain to be separated. This information can be used to determine the conformational equilibria of the alkyl chain under the influence of the nematic field created by surrounding molecules. Transport properties have been examined by calculating diffusion coefficients in directions both parallel and perpendicular to the nematic director. All properties calculated using the pseudomolecular potential are compared with those obtained from the more complete atom–atom potential to assess the validity of the simplified approach.

Structural properties of mixtures of highly asymmetrical electrolytes and uncharged particles using the hypernetted chain approximation

We have solved the Ornstein–Zernike equation in the hypernetted chain (HNC) approximation for several mixtures of electrolytes and uncharged hard spheres. The mixtures that we studied range from a simple restricted primitive model plus hard spheres of the same size to highly asymmetric electrolytes plus hard spheres of different sizes. We monitored the radial distribution function and thermodynamic properties. We find that the presence of neutral particles changes the nature of the interaction between the charged particles. We also find a strong correlation between nonelectrostatic and electrostatic contributions to the free energy of the mixtures. Potential applications of this approach to the study of protein solubility in solutions of nonionic polymers are discussed.

Ultrasonic scattering from spherical shells including viscous and thermal effects

An analysis for sound scattering and attenuation by shell structures immersed in fluids is outlined. While the form of the analysis permits easy comparison with previous results for simple spheres, it includes novel features of viscoelasticity in the shell and core materials (which may be fluid or solid), viscosity in the suspending fluid, and thermal effects. The computational procedure adopted is outlined with particular reference to the avoidance of numerical instabilities at very low and very high values of ‘‘ka.’’ The testing of the program by comparison with previous results on simpler systems is reported, and a limited selection of numerical results is given. The program has been used successfully over the range of ka values between 10−6 and 200, its robustness needs closer definition.

Strain measurements inside solids subjected to lithotripter pulses

To study the direct stress wave effects on the fragmentation of kidney stones or gallstones during lithotripsy, it is important to know the evolution of the stress state inside concretions subjected to lithotripter pulses. Knowledge of these stress fields can be used, along with measurements of the mechanical properties of the stone, to predict locations and modes of failure. A technique of implanting monocrystalline silicon strain gauges within plaster concretions to obtain information about these internal stress fields was developed. Concretions of simple geometries, i.e., disks and spheres, were chosen for this initial study so that the reflections from the boundaries can be more easily identified and compared with theoretical models. Experimental results were obtained for both spherically diverging and focused shock wave sources. Theoretical models based on geometrical acoustics were developed for a spherical wave front incident on a disk and on a sphere. Predictions from these models match well with the experimental results. In addition, the caustic surfaces for a spherically diverging wave incident on a sphere are present. [Work supported by NIH Grant No. DK39796.]

Description of the sound scattering and radiation from compact but complex bubble distributions using multipole expansions

Dynamic bubble distributions in liquids and their acoustic properties are important in a large variety of applications ranging from the measurement of nitrogen bubbles in blood, fish schools, to clouds from breaking waves. Unlike individual bubbles, these distributions maintain their compactness by viscous and hydrodynamic vorticity. The specific case of compact distributions that have complex shapes may be treated by the use of multipole expansions. This paper discusses the application of multipole expansions to complex shapes in general and compares the first-order radiation and scattering fields from simple geometrical shapes, spheres, cylinders, and ellipsoids. The paper shows that when the regions are acoustically compact the lowest-order radiation from these features can be described by a modified Minneart formula describing the net volume fluctuation. In the case of noncompact distributions scattering regimes are shown to be delineated by several nondimensional numbers.

A density functional theory for polymers: Application to hard chain–hard sphere mixtures in slitlike pores

A density functional theory for polymer fluids is derived. The form of the theory is identical to a continuum self-consistent-field theory but we show that with the correct ‘‘mean field,’’ the theory is exact. We apply the theory to a polymer fluid made up of tangential hard spheres and borrow from a successful density functional theory for simple hard spheres to obtain a nonlocal functional expression for this mean field. The latter depends only upon the monomer density. This approximation is used to treat the problem of a mixture of such polymers and simple hard spheres, contained in slitlike pores. Comparison with simulations show that the theory, though simple in structure, and containing a single adjustable parameter, is surprisingly accurate.

Evidence of melanogenesis in porcine retinal pigment epithelial cells in vitro

Several weeks after porcine retinal pigment epithelial (RPE) cell cultures attain confluence, macroscopically visible brown foci appear. The cuboidal cells that form the foci contain numerous phase dark granules that do not exhibit the autofluorescence characteristic of lipofuscin. The data described here indicate that the granules are melanosomes. Electron microscopy revealed three types of electron-dense granules in these cells: simple spheres 0·3–0·5 μm in diameter, large spheres 1–2 μm in diameter, and lysosomal aggregations of the smaller spheres. The matrix of both spheres is composed of 40-nm microvesicles that were also found free in the cytoplasm and aggregated within vacuolar structures. Reversed-phase high-performance liquid chromatography of RPE cells and their media detected melanogens, i.e. intermediates of melanin biosynthesis, including several indole derivatives. The porcine RPE cultures therefore may be a useful system for studying melanogenic regulation.

Critical evaluation of the application of direct energy transfer in probing the morphology of porous solids

The decay of an initially excited donor due to the presence of acceptor molecules embedded in porous silica gels has been studied. The time evolution of the decay process has been related to the geometrical restrictions imposed on the participating molecules by the porous structure of the silicas. Fractal and regular geometrical shape models have been confronted with experimental findings. We conclude that for silica gels simple pore geometries, i.e., spheres and cylinders, account well for the relaxation behavior. The decay patterns exhibit temporal crossovers typical of dynamics in restricted geometries.

Spherical clusters of simple metals: Madelung energies and structures

The Madelung energies of simple metal spheres are calculated for bcc, fcc, and hcp structures as well as for fully relaxed structures. It is found that for clusters of up to 40 atoms the structure generally does not have the symmetry of any simple lattice. The variation of the structural part of the total energy is shown to be slightly smaller than the variation arising from the filling of discrete single-electron energy levels.

Measurements of the acoustic backscatter of manganese nodules

The acoustic backscatter of eight well-curated ferromanganese nodules has been measured in 1 °C seawater at frequencies from 45 to 167 kHz. The nodules have diameters from 37 to 121 mm and are thought to be representative of the Cu–Ni–Co-rich nodules from the area around 14° 40′ N, 125° 25′ W (DOMES site C). They had been collected in box cores on the Echo 1 expedition and were kept refrigerated and water soaked in air-tight plastic bags. Acoustic backscatter variations of over 10 dB were observed while the nodule was rotated 10° to 30° about one of its principal axes. The complicated fine structure, as well as the target strength, makes it clear that nodules cannot be modeled as simple spheres.

Cytodiffrentiation in the accessory glands of Tenebrio molitor. VI. A congruent map of cells and their secretions in the layered elastic product of the male bean-shaped gland.

The morphology of the bean-shaped accessory glands (BAGs) of males of Tenebrio molitor is described. All cells in the secretory epithelium are long and narrow (300-400 mμ × 5 mμ). The seven types of secretory cells are distinguished from one another by the morphology of their secretory granules. Granule substructure varies from simple spheres with homogeneous electrondense contents to complex forms with thickened exterior walls or with crystalline and membranous contents. Individual cell types were mapped by staining whole glands with Oil Red O, and the cell distributions were confirmed by wax histology and ultramicroscopy. The secretions of all seven cell types form a secretory plug composed of seven layers. During mating, the secretory plug from each BAG is forced into the ejaculatory duct by contractions of a sheath of circular muscle. The mirror image plugs from symmetrical BAGs fuse and are transformed into the wall of the spermatophore.

Fuel pellets and optical systems for inertially confined fusion

Current laser-driven ICF targets are complex sets of concentric spherical shells made from a variety of materials including the fuel (e.g., deuterium-tritium), glass, beryllium, gold, polymeric materials, organo-metallics, and several additional organic and inorganic materials depending on the particular experiments to be done. While we don't yet know what the reactor targets will be exactly, there is little reason to believe they will be just simple, low quality glass shells containing DT gas or simple spheres of deuterated polyethylene or other fuel. Consequently, we consider many of the current targets, materials, and fabrication techniques to be applicable to the long range problems of ICF reactor target fabrication. Many of our current material problems and fabrication techniques are discussed and various quality factors are presented in an attempt to bring an awareness of the possible fusion reactor target materials problems to the scientific and technical community.We should note that “target]” and “pellet” are used interchangeably and do not have any subtle variational significances.

Cross sectionally simple spheres can be wild

The first part of this paper supplements earlier work of the first-named author by exhibiting an example of a wild n-sphere Σ in E n+1 ( n⩾4) for which each horizontal n-dimensional hyperplane of E n+1 that does meet Σ intersects it either in a point or in an ( n − 1)-sphere that is flatly embedded in the hyperplane. The second part sets forth an improved criterion for detecting the n-cell ( n ≠ 4) based upon properties of slices determined as inverse sets associated with maps of a space to an interval.

Statistical mechanics of small chain molecules in liquids. I. Effects of liquid packing on conformational structures

When a chain molecule can be viewed as a collection of overlapping spherical groups, the effect of a solvent on the conformational structure of the chain molecule is described by the distribution function for the cavity particles associated with the spherical groups. This article discusses the calculation of the cavity distribution function for n-butane disolved in various apolar solvents: the liquids carbon tetrachloride, n-butane, and n-hexane. We consider the common picture where the CH3 and CH2 groups in n-butane are simple spheres. For that model, the cavity distribution function is a four-point correlation function. We find that the superposition approximation for the four-point function, while qualitatively correct, overestimates the effects of the solvent. An alternative scheme, which is called the two cavity model, yields results that agree quantitatively with a computer simulation study of liquid n-butane. We find that a solvent medium produces significant shifts in the conformational equilibrium of n-butane from that found in the gas phase. This phenomenon is the result of the nature of the local packing of solvent molecules neighboring the solute species under investigation. The conformational equilibrium is sensitive to this packing. The bulk packing fractions (molecular density times the volume of the molecule) of the liquids CCl4 and C4H10 are nearly identical. Even so there are noticeable differences between the intramolecular structure of n-butane in liquid carbon tetrachloride and in the neat liquid. Previous ideas on conformational equilibria have ignored the importance of steric (i.e., liquid packing) effects, and have assumed that solvent shifts in conformational structures can be attributed entirely to dielectric effects. Our calculations show that this assumption is wrong. The n-butane molecule contains no significantly polar groups. yet solvent media produce substantial shifts. For example, the trans–gauche equilibrium constant, xg/xt, for n-butane in the gas phase at room temperature is roughly 0.5, while we find it is about 1.0 when n-butane is dissolved in liquid CCl4 at the same temperature and 1 atm pressure. We discuss why the phenomenon has been overlooked, and suggest experiments to document its existence.

Folding and stability of helical proteins: Carp myogen

In this work we use our very simple general representation of protein structures to study the mainly helical protein carp myogen. The representation, which treats the amino acid side-chains as simple spheres, is further simplified by rigidly fixing residues in α-helices. With this model we are able to reproduce the geometry and energetic stability of the native myogen conformation. Studies of the formation of α-helical sub-assemblies showed that the simulated folding of two and four-helix systems worked well, reaching compact native-like conformations with a good rate of success. Greater problems were encountered with the whole molecule (six helices), possibly due to the omission of entropic effects or to simulating the folding too rapidly. Finally, studies of the conformation of a pair of helices when isolated and when part of the whole molecule native conformation showed that long-range interactions have an unexpectedly strong influence on the conformation of the pair of helices.

Dissociation of hydrogen molecules in collisions with light alkali ions.: III. Comparison of experiment with a simple hard spheres model

A simple hard spheres model is used to calculate cross sections for the dissociation of a light homonuclear molecule in collisions with an alkali ion. The results are analyzed in terms of the relative contribution of different types of binary collision sequences. In agreement with experiment the number of “simple” spectator collisions is found to depend strongly on the effective collision diameter. The model is shown to break down in the simulation of certain collision sequences and thus it cannot explain the measured inelastic differential cross section at all scattering angles. The model does work, however, for backward large angle scattering enar 180° for which the largest amount of experimental data is available. The model is used to extract potential parameters for the ion—atom two body interaction potential. These are in reasonable agreement with previous determinations.

Cross sectionally simple spheres

Cross sectionally simple spheres

The bacteriophages of Pseudomonas aeruginosa; filtration measurements and electron microscopy.

Preliminary observations in a systematic study of fifteen bacteriophages isolated fromPseudomonas aeruginosaare described. The evidence as to size, morphology and plaque appearance indicates that this group of phages comprises several distinct types. The electron microscope reveals some of the phages to be simple spheres, but the majority are tailed particles.The importance of this group in the study of the phenomenon of lysogenicity is pointed out.

The reactions of bacterial viruses with their host cells

In its early stages the study of a sector of nature may be divided into two branches. In one we inquire what an object under investigation is; we want to know its morphology and its relation to other more or less similar objects. In the other branch we study what the object does and how it came to be what it is. Thus in chemistry we have molecular structure on the one hand and kinetics of reaction on the other. In biology, anatomy and embryology may be taken as examples of the two points of view. As a science progresses certain relations between structure and function begin to emerge, and eventually the pursuit of these relations may become the major interest in the field. The study of viruses is a very young science indeed. In recent years much progress has been made toward a better understanding of those phases of the virus problem concerned with the infectious agent or virus particle (7). Improved methods of isolation, culture, concentration and assay have made purified preparations of many viruses available in relatively large quantities for physical and chemical characterization. Application of the ultracentrifuge and diffusion techniques gives indirect evidence of the mean sizes and shapes of virus particles in solution; the electron microscope has made possible direct observation of sizes and shapes of individual particles in the dry state (7, 8, 53, 56, 68, 69, 72) ; and x-ray diffraction has given clues to the atomic architecture of certain plant virus particles (11). It has turned out that this segment of biological material includes particles as small as 10 mu and as large as 200 mu in diameter. The morphologies of the viruses range from relatively large cell-like structures (vaccinia), some of them being tadpole-shaped (T2 bacteriophage), to simple rods (tobacco mosaic) and spheres (bushy stunt). On the other hand, the particles of any particular strain of virus exhibit a remarkable uniformity in size and structure.