Radius Fluctuations Research Articles

Quantitative theory of the globule-to-coil transition. 2. Density-density correlation in a globule and the hydrodynamic radius of a macromolecule

The macromolecule properties determined by the pair density-density correlation function are considered. This function is calculated in the framework of mean field Lifshitz's theory. Using the correlation function, the hydrodynamic radius of a macromolecule is found in the Kirkwood approximation. The value of fluctuations in the macromolecule radius of gyration is calculated in the region of the globule-to-coil transition, which is connected with a sharp change in the fluctuational regime. The existence of a maximum of fluctuations in the transition region is shown

Flame surface properties of premixed flames in isotropic turbulence: Measurements and numerical simulations

An experimental and theoretical investigation of free turbulent premixed flames propagating in isotropic turbulence at neutrally stable preferential diffusion conditions is described. Experiments were limited to the wrinkled thin laminar flamelet regime and involved mixtures of hydrogen, air, and nitrogen ignited within a fan-stirred combustion chamber. Measurements included flame tomography for flame surface statistics and two-point laser velocimetry for unburned gas turbulence properties. Flame surface properties were numerically simulated using a two-dimensional flame propagation algorithm combined with statistical time series simulation of unburned gas velocities along the flame surface. Measurements showed progressively increasing flame radius fluctuations, flame surface fractal dimensions, and turbulent/laminar flame perimeters with increasing mean frame radius. The rate of increase of these properties all increased with increasing turbulence intensities relative to laminar flame speed. Simulated flame properties duplicated these trends but underestimated the effects of turbulence—a deficiency mainly attributed to the limitations of a two-dimensional simulation. Extension of the method to a three-dimensional simulation, to obtain a more definitive evaluation of the simulation, appears to be computationally feasible.

Stochastic simulation of free turbulent premixed flames in isotropic turbulence

A theoretical investigation of free turbulent permixed flames in isotropic turbulence is described, limited to the wrinkled thin laminar flamelet regime at neutrally-stable preferential diffusion conditions with negligible effects of quenching. The objective was to develop a computationally tractable three-dimensional time-dependent simulation of flame surface properties, capable of treating turbulence Reynolds numbers typical of experiments and practical flames. The approach involved statistical time series simulation of unburned gas velocities in conjunction with a flame advection and propagation algorithm. The following properties of the unburned gas were simulated, assuming that unburned gas turbulence properties were not affected by the flame: mean velocities due to volumetric expansion at the flame surface, and the Gaussian probability density functions and the spatial and temporal correlations of velocity fluctuations, while satisfying the requirement that cross correlations of velocity fluctuations are zero for isotropic turbulence. Predictions were evaluated using existing measurements for free flames propagating in hydrogen/oxygen/nitrogen mixtures having turbulence intensities relative to laminar burning velocities of 0.48–1.60 and turbulence Reynolds numbers of 1965–4195. Both two- and three-dimensional/time-dependent simulations yielded correct trends of measured flame surface statistics. This included the temporal variation of mean flame radius, r.m.s. flame radius fluctuations, and the average perimeter and fractal dimensions of the wrinkled flame surfaces for various relative turbulence intensities. However, performance of the two-dimensional simulation was less satisfactory because flame surface distortion by turbulence in one coordinate direction was suppressed. Additionally, the three-dimensional simulations underestimated effects of turbulence to some extent, a deficiency attributed to effects of volumetric expansion at the flame surface on unburned gas velocities, with approximations used to treat spatial and temporal correlations of velocity fluctuations in the unburned gas being possible contributing factors. Nevertheless, extension of the three-dimensional/time-dependent simulation to treat other flame configurations, as well as effects of quenching and preferential diffusion, appears to be warranted and is feasible due to the computational efficiency of the velocity simulation.

Sedimentation, diffusion, and Taylor dispersion of a flexible fluctuating macromolecule: The Debye–Bueche model revisited

The role of hydrodynamic flexibility stemming from a lack of configurational rigidity in the sedimentary and dispersive transport of macromolecules in dilute polymer solutions is analyzed within the framework of generalized Taylor dispersion theory. A macromolecular chain is modeled as a thermally fluctuating porous Brownian spongelike sphere which—in contrast with the classical investigations of Debye–Bueche and Brinkman for the rigid porous sphere case—is allowed to undergo thermal fluctuations in size (assumed governed by a Hookean elastic potential). Our results show an increase of up to about 20% in the average translational mobility of the flexible (size-fluctuating) sphere above that of the comparable rigid Debye–Bueche/Brinkman sphere (of equilibrium preaveraged radius). Coupling between mobility variations (arising from instantaneous fluctuations in sphere radius) and diffusive sampling of such sphere radii in size space, respectively, gives rise to a ‘‘Taylor’’ dispersion mechanism, which enhances the diffusivity of the macromolecule above and beyond its purely molecular value. Indeed, the dispersivity (dyadic) of the sedimenting sphere is shown to be anisotropic, possessing a value different from its (mean) molecular diffusivity in the direction of net sedimentation. Both sedimentation and dispersion effects associated with size fluctuations are shown to be maximized at finite, intermediate values of the nondimensional sponge stiffness parameter S, rather than being monotonically decreasing functions of S. The relative importance of both effects increase with decreasing permeability of the sphere. With an increasing number (N≫1) of monomer units composing the chain, the isotropic (molecular) portion of the dispersivity dyadic decreases like N−1/2, whereas the anisotropic Taylor-dispersion portion, which is exclusively associated with the size fluctuations, increases like N3. The latter contribution, which is negligible for ordinary gravitational settling (owing to the smallness of the relevant Langevin parameter), may, however, become significant for ultracentrifugation of polymer solutions composed of long (N>105) macromolecular chains.

Influence of the gas flow turbulence on the angular divergence of radiation emitted from a plane-parallel optical resonator

An investigation was made of the influence of the effects of wave refraction by turbulent pulsations of the gas flow on the characteristics of the wavefront and on the angular divergence of radiation emitted from a plane-parallel optical resonator. The equation for the mutual coherence function Γ (x, x'; z) was solved numerically in the approximation of a parabolic equation with Markov (in terms of the longitudinal correlation radius) fluctuations of the permittivity. The calculations were carried out using the method of splitting by parameters. It is shown that enhancement of the turbulence flattens out the distribution of the field on the mirror and increases the angular divergence. When the angular divergence is governed by turbulent effects, the magnitude of this divergence increases also on increase in the wave number.

児童公園の利用圏域の変動

My object in this paper is to make it clear that to what extent the service radius of the park for children is affected by the area of park, and by the sex distinction of children, and by the distinction of school years. So, at first, I named "the base point of playing" for the house that is the nearest to the spot of each playing, among houses of a child own and his friends' whom played with. And, I took the tendensy of the relation between the distribution of distances from "each base point of playing" to the nearest park, and each percentage of the number of play, such as play in parks or play on roads or play in vacant lots, to the total number of play. And, I classified the area of park to 7 ranks by the tendensy of that relation. On each classified rank of park, the service radius of the park for children was taken as shown in Table 8. And, the next, on each classified rank of park, I took the service radii of the park for children in such cases as girls are playing, as boys are playing, as each school year children are playing. The results in this study are as follows; (1) The service radius is affected by the area of the park to such extent as shown in Table 8. But, the fluctuation of the service radius is small. On each classified rank of park, the service radius is included in 80 + 40 meters. (2) The service radius is not affected by the sex distinction of children, neither by the distinction of school years. (Table 12)

The effect of crystal radius fluctuations on the stress field in LEC gallium arsenide

Calculations of the shear stress field in LEC Gallium Arsenide have been carried out in which the crystal radius was systematically changed during growth. Various combinations of wavelength and amplitude of fluctuations were considered both in the bulk crystal and the seeding cone. For the bulk crystal, the maximum shear stress is shown to increase as the amplitude of the fluctuations increases and the wavelength decreases. For fluctuations with wavelengths less than 20 mm, the shear stress increases hyperbolically with decreasing wavelength. Fluctuations in radius in the seeding cone result in higher stresses in the cone, bu these stresses do not reach the stresses in the bulk crystal.

Finite-temperature instability for compactification.

We consider finite temperature effects upon theories with extra dimensions compactified via vacuum stress energy (Casimir) effects. For sufficiently high temperature, a static configuration for the internal space is impossible. At somewhat lower temperatures, there is an instability due to thermal fluctuations of radius of the compact dimensions. For both cases, the Universe can evolve to a de Sitter-like expansion of all dimensions. Stability to late times constrains the initial entropy of the universe. 28 refs., 1 fig., 2 tabs.

A numerical study of discrete euclidean polyakov surfaces

The results of a computer experiment simulating the behaviour of a version of a discrete Polyakov surface are presented. A non-trivial variation of the fractal dimension of the surface with the dimensionality of the embedding space is found. Fluctuations of the gyration radius and of the coordination number are also considered.

Microdeformation losses of single-mode fibers

In this paper, we consider the scattering losses of single-mode fibers that are caused by microdeformations such as microbends of the fiber axis and random fluctuations of the fiber core diameter. Since very little is known about the statistics of microdeformations of actual fibers, we assume that the autocorrelation functions of random bends and random core diameter fluctuations are Gaussian, characterized by the rms deviation and the correlation length of the random function. We consider single-mode fibers with step, parabolic, and triangular (linear) refractive-index profiles and reach the following conclusions: (1) Whereas for equal (large) mode radii the microbending losses of all three fiber types are the same, losses due to random core diameter fluctuations can be three times as high in step-index fibers as in triangular-index fibers. Since triangular-index fibers have sometimes been observed to have lower scattering losses than step-index fibers, one might conclude that, in these cases, excess losses may be caused by random radius fluctuations rather than by microbends. (2) Radial refractive-index ripples, which tend to be present in the deposited claddings of single-mode fibers, seem unlikely to be a major source of microdeformation losses. (3) The wavelength dependence of microdeformation losses depends strongly on the value of the correlation length of the Gaussian autocorrelation function of the fiber deformations. If the correlation length is of the same order of magnitude as the fiber radius, the losses are only slightly wavelength dependent. For very long correlation lengths the losses are very much smaller (for the same rms variation of the random functions), but they become strongly wavelength dependent, increasing sharply with increasing wavelength.

Small angle neutron scattering study of structural heterogeneities in a-Si : H

Small angle neutron scattering measurements have been made on pure, hydrogenated or deuterated samples of amorphous silicon. The scattered intensity from the sputtered films indicate density fluctuations of average radius of gyration of about 125 Å. The presence of a ring at 0.22 Å −1 on the diffraction pattern obtained from a-Si : H suggests a possible correlation length of about 30 Å.

Mode power distribution in optical fibres with fluctuation in physical parameters and application to backscattering signal analysis

The evolution of mode power distribution in fibres with fluctuations of physical parameters is investigated. The analysis is applied to the interpretation of backscattering trace. Rigorous expressions of backscattering power in the presence of fluctuations of fibre core radius and maximum NA are provided in many common cases.

Scattering and Absorption Losses of Multimode Optical Fibers and Fiber Lasers

We present an approximate theory of loss coefficients for modes of step-index fibers with various types of distortions and for fibers with lossy claddings. The fiber irregularities are assumed to be sinusoidal and random variations of the core-cladding interface. Formulas for the loss coefficients are presented and plotted for different values of the compound mode number M. For fiber lasers, we plot the loss coefficients as functions of the mirror tilt angles. We consider as an example a Nd-YAG fiber laser with refractive index n 1 = 1.8 and a core radius of a = 40 µm operating at a wavelength of λ = 1.06 µm. For this example, we find that radiation losses are caused by Fourier components of fiber irregularities in the spatial wavelength range between 0.4 and 1.3 µm. Intrinsic losses may be as low as 2α = 10−3 cm−1. It is thus desirable to limit scattering losses to values below 10−3 cm−1. This requirement imposes tolerance restrictions of 0.01 µm on the permissible core radius fluctuations. For core radius fluctuations of this order of magnitude, mirror tilts should not exceed approximately 5 degrees. Cladding losses are not critical, but their influence on laser losses depends on the refractive index ratio of the core and cladding materials. Tolerable cladding losses may range from 10 to 300 cm−1.

Radiation losses of the HE_11 mode of a fiber with sinusoidally perturbed core boundary

The radiation losses of the HE(11) mode of a fiber with sinusoidal radius fluctuations are calculated in the weak guidance approximation. The loss formula is derived by means of the volume current method and also by using coupled mode theory. The result presented here extends earlier results to the case of radiation escaping nearly perpendicular to the fiber axis.

On Polymer Dynamics. II

The viscosity, storage and loss moduli, fluctuations in length, Lagrange multiplier, pair-correlation functions, and radius of gyration are evaluated for the model of Harris and Hearst.

The Relation of the Water Content of Loquat Trees to Various Weather in Early Spring

Since it is said that evergreen fruit trees, the water absorption of which is very much reduced at low temperature, often suffer more from the dryness of winter wind than from its coldness, the water content of the Tanaka loquat tree was investigated in the cold season. The water content of the leaves was measured with the impedance bridge which had special measuring terminal plates, and that of the trunk was measured with a hundredth millimeter dial guage and indicated in terms of radius fluctuation. The results of the investigation was summarized below.1. The daily water content of the leaves reached the minimum at 4 p.m. and the maximum at 2 a.m., the range of fluctuation being 2.5 percent. That of the trunk showed much the same change.2. In the daytime, the water content of the leaves of the outer crown was larger than that of the inner crown and reached the minimum at noon. The water content of the leaves of the inner crown reached the minimum 6 hours later, and so did that of the trunk 2 hours later than that of the leaves of the outer crown. The similar type of fluctuation was observed in the water content of those three.3. The water content of the leaves was largest on rainy day and smallest on windy day, the difference being about 4 percent at the largest. The water content of the leaves on fine day was about 1 percent larger than on windy day. It may be said that the loquat leaves have so numerous hairs that they can keep transpiration down a little. It may be for this reason that the water in the leaves did not show great change in amount. It is suggested, therefore, that the loquat trees do not suffer very much from dry winter wind in warm regions.