A self-similar expansion model for use in solar wind transient propogation studies

Since the advent of wide-angle imaging of the inner heliosphere, a plethora of techniques have been developed to investigate the three-dimensional structure and kinematics of solar wind transients, such as coronal mass ejections, from their signatures in single- and multi-spacecraft imaging observations. These techniques, which range from the highly complex and computationally intensive to methods based on simple curve fitting, all have their inherent advantages and limitations. In the analysis of single-spacecraft imaging observations, much use has been made of the fixed φ fitting (FPF) and harmonic mean fitting (HMF) techniques, in which the solar wind transient is considered to be a radially propagating point source (fixed φ, FP, model) and a radially expanding circle anchored at Sun centre (harmonic mean, HM, model), respectively. Initially, we compare the radial speeds and propagation directions derived from application of the FPF and HMF techniques to a large set of STEREO/Heliospheric Imager (HI) observations. As the geometries on which these two techniques are founded constitute extreme descriptions of solar wind transients in terms of their extent along the line of sight, we describe a single-spacecraft fitting technique based on a more generalized model for which the FP and HM geometries form the limiting cases. In addition to providing estimates of a transient’s speed and propagation direction, the self-similar expansion fitting (SSEF) technique provides, in theory, the capability to estimate the transient’s angular extent in the plane orthogonal to the field of view. Using the HI observations, and also by performing a Monte Carlo simulation, we assess the potential of the SSEF technique.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

The population genetic structure of clonal organisms generated by exponentially bounded and fat-tailed dispersal

Long distance dispersal (LDD) plays an important role in many population processes like colonization, range expansion, and epidemics. LDD of small particles like fungal spores is often a result of turbulent wind dispersal and is best described by functions with power-law behavior in the tails ("fat tailed"). The influence of fat-tailed LDD on population genetic structure is reported in this article. In computer simulations, the population structure generated by power-law dispersal with exponents in the range of -2 to -1, in distinct contrast to that generated by exponential dispersal, has a fractal structure. As the power-law exponent becomes smaller, the distribution of individual genotypes becomes more self-similar at different scales. Common statistics like G(ST) are not well suited to summarizing differences between the population genetic structures. Instead, fractal and self-similarity statistics demonstrated differences in structure arising from fat-tailed and exponential dispersal. When dispersal is fat tailed, a log-log plot of the Simpson index against distance between subpopulations has an approximately constant gradient over a large range of spatial scales. The fractal dimension D-2 is linearly inversely related to the power-law exponent, with a slope of similar to -2. In a large simulation arena, fat-tailed LDD allows colonization of the entire space by all genotypes whereas exponentially bounded dispersal eventually confines all descendants of a single clonal lineage to a relatively small area.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

The Brownian traveller on manifolds

We study the inuence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the at case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the at case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

Coalescence of particles by differential sedimentation

We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a size-dependent terminal velocity. They are either allowed to merge whenever they cross or there is a size ratio criterion enforced to account for collision efficiency. Such a system may be described, in mean field approximation, by the Smoluchowski kinetic equation with a differential sedimentation kernel. We obtain self-similar steady-state and time-dependent solutions to the kinetic equation, using methods borrowed from weak turbulence theory. Analytical results are compared with direct numerical simulations (DNS) of moving and merging particles, and a good agreement is found.

Fast training of self organizing maps for the visual exploration of molecular compounds

Visual exploration of scientific data in life science area is a growing research field due to the large amount of available data. The Kohonen’s Self Organizing Map (SOM) is a widely used tool for visualization of multidimensional data. In this paper we present a fast learning algorithm for SOMs that uses a simulated annealing method to adapt the learning parameters. The algorithm has been adopted in a data analysis framework for the generation of similarity maps. Such maps provide an effective tool for the visual exploration of large and multi-dimensional input spaces. The approach has been applied to data generated during the High Throughput Screening of molecular compounds; the generated maps allow a visual exploration of molecules with similar topological properties. The experimental analysis on real world data from the National Cancer Institute shows the speed up of the proposed SOM training process in comparison to a traditional approach. The resulting visual landscape groups molecules with similar chemical properties in densely connected regions.

New strings for old : the role of similarity processing in an incidental learning task

This paper reports three experiments that examine the role of similarity processing in McGeorge and Burton's (1990) incidental learning task. In the experiments subjects performed a distractor task involving four-digit number strings, all of which conformed to a simple hidden rule. They were then given a forced-choice memory test in which they were presented with pairs of strings and were led to believe that one string of each pair had appeared in the prior learning phase. Although this was not the case, one string of each pair did conform to the hidden rule. Experiment 1 showed that, as in the McGeorge and Burton study, subjects were significantly more likely to select test strings that conformed to the hidden rule. However, additional analyses suggested that rather than having implicitly abstracted the rule, subjects may have been selecting strings that were in some way similar to those seen during the learning phase. Experiments 2 and 3 were designed to try to separate out effects due to similarity from those due to implicit rule abstraction. It was found that the results were more consistent with a similarity-based model than implicit rule abstraction per se.

The phenology and potential for self-pollination of two Australian monoecious fig species

In this preliminary study, the reproductive phenology of two monoecious fig species, Ficus racemosa and F. rubiginosa, was examined in tropical Australia. Syconia (inflorescences) occurred on both species all year round, but pre-floral and interfloral syconia were much commoner than the wasp-receptive and wasp-emitting phases in both species. The temporal overlap of the wasp-receptive and wasp-emitting phases on a single tree indicated that self-pollination was possible in both species and that pollinators may sometimes persist through multiple generations on one tree. This sexual phase overlap was commoner in F. rubiginosa than in F racemosa. The two species also differed in their general within-tree asynchrony, with a higher diversity of phases on F. rubiginosa than on F. racemosa. The time from syconium initiation to ripening was very similar in F. rubiginosa (mean = 48.51 days) and F. racemosa (mean = 43.53 days). However, there was much more variation within and between trees for F. rubiginosa. In addition, the wasp-receptive phase was found to last up to 5 days (rnean = 4.38) in F. rubiginosa. Such longevity should contribute substantially to local pollinator population persistence. Future work should use genetic studies to determine whether self-pollination is common in these fig species.

The role of protecting groups in the formation of organogels through a nano-fibrillar network formed by self-assembling terminally protected tripeptides

A series of eight synthetic self-assembling terminally blocked tripeptides have been studied for gelation. Some of them form gels in various aromatic solvents including benzene, toluene, xylene, and chlorobenzene. It has been found that the protecting groups play an important role in the formation of organogels. It has been observed that, if the C-terminal has been changed from methyl ester to ethyl ester the gelation property does not change significantly (keeping the N-terminal protecting group same), while the change of the protecting group from ethyl ester to isopropyl ester completely abolishes the gelation property. Similarly, keeping the identical C-terminal protecting group (methyl ester) the results of the gelation study indicate that the substitution of N-terminal protection Boc-(tert-butyloxycarbonyl) to Cbz-(benzyloxycarbonyl) does change the gelation property insignificantly, while the change from Boc- to pivaloyl (Piv-) or acetyl (Ac-) group completely eliminates the gelation property. Morphological studies of the dried gels of two of the peptides indicate the presence of an entangled nano-fibrillar network that might be responsible for gelation. FTIR studies of the gels demonstrate that an intermolecular hydrogen bonding network is formed during gelation. Results of X-ray powder diffraction studies for these gelator peptides in different states (dried gels, gel, and bulk solids) reflected that the structure in the wet gel is distinctly different from the dried gel and solid state structures. Single crystal X-ray diffraction studies of a non-gelator peptide, which is structurally similar to the gelator molecules reveal that the peptide forms an antiparallel beta-sheet structure in crystals. (c) 2007 Elsevier Ltd. All rights reserved.

Self-assembly of two-component gels: stoichiometric control and component selection

Two-component systems capable of self-assembling into soft gel-phase materials are of considerable interest due to their tunability and versatility. This paper investigates two-component gels based on a combination of a L-lysine-based dendron and a rigid diamine spacer (1,4-diaminobenzene or 1,4-diaminocyclohexane). The networked gelator was investigated using thermal measurements, circular dichroism, NMR spectroscopy and small angle neutron scattering (SANS) giving insight into the macroscopic properties, nanostructure and molecular-scale organisation. Surprisingly, all of these techniques confirmed that irrespective of the molar ratio of the components employed, the "solid-like" gel network always consisted of a 1:1 mixture of dendron/diamine. Additionally, the gel network was able to tolerate a significant excess of diamine in the "liquid-like" phase before being disrupted. In the light of this observation, we investigated the ability of the gel network structure to evolve from mixtures of different aromatic diamines present in excess. We found that these two-component gels assembled in a component-selective manner, with the dendron preferentially recognising 1,4-diaminobenzene (>70%). when similar competitor diamines (1,2- and 1,3-diaminobenzene) are present. Furthermore, NMR relaxation measurements demonstrated that the gel based oil 1,4-diaminobenzene was better able to form a selective ternary complex with pyrene than the gel based oil 1,4-diaminocyclohexane, indicative of controlled and selective pi-pi interactions within a three-component assembly. As such, the results ill this paper demonstrate how component selection processes in two-component gel systems call control hierarchical self-assembly.

Coordination-driven self-assembly of a novel carbonato-bridged heteromolecular neutral nickel(II) triangle by atmospheric CO2 fixation

Formation of a quasi-symmetrical mu(3)-carbonato-bridged self-assembled heteromolecular triangle of Ni(II), [(mu(3)-CO3){Ni-2(salmeNH)(2)(NCS)(2)}[Ni(salmeNH(2))(2)]center dot Et2O center dot H2O (HsalmeNH = 2-[(3-methylamino-propylimino)-methyl]-phenol) involves atmospheric CO2 uptake in a neutral medium, by spontaneous self-reorganization of the starting mononuclear Ni(II)-Schiff-base complex, [Ni(salmeNH)(2)]. The environment around Ni(II) in two of the subunits is different from the third one. The starting complex, (Ni(salmeNH)(2)], and one of the possible intermediate species, [Ni(salmeNH(2))(2)(NCS)(2)], which has a very similar coordination environment to that in the third Ni(II) center, have been characterized structurally. A plausible mechanism for the formation of such a triangle has also been proposed. The compound shows a very strong antiferromagnetic coupling. Fit as a regular triangular arrangement gave J = -53.1, g = 2.24, and R = 1.5 x 10(-4).