scholarly journals The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Bin Ma ◽  
Xiaofei Lv ◽  
Jun Gong
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Low Frequency ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life displays a consistent power-law rules for inter- and intra-taxonomic levels. The values of fractal dimension for both inter- and intra-taxonomic levels were different among different kingdoms. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with low frequency; the proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the abundance of subtaxa in taxa with small and large sizes can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. These results emphasize the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups.

scholarly journals The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Xiaofei Lv ◽  
Yuping Wu ◽  
Bin Ma
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Dimensions ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life display a consistent power-law rules for inter- and intra-taxonomic levels, but the fractal dimensions were different among different kingdoms. The fractal dimension of hierarchical structure (Dr) is 0.873 for the entire tree of life, which smaller than the values of Dr for Animalia and Plantae but greater than the values of Dr for Fungi, Chromista, and Protozoa. The hierarchical fractal dimensions values for prokaryotic kingdoms are lower than for other kingdoms. The Dr value for Viruses was lower than most eukaryotic kingdoms, but greater than prokaryotes. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with large subtaxa size. The proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the distribution of subtaxa in taxa can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. Our study determined the fractal dimensions for inter- and intra-taxonomic levels of the present tree of life. These results emphases the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups and skewness of taxa with large subtaxa size.

scholarly journals The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Bin Ma ◽  
Xiaofei Lv ◽  
Jun Gong
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Dimensions ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life display a consistent power-law rules for inter- and intra-taxonomic levels, but the fractal dimensions were different among different kingdoms. The fractal dimension of hierarchical structure (Dr) is 0.873 for the entire tree of life, which smaller than the values of Dr for Animalia and Plantae but greater than the values of Dr for Fungi, Chromista, and Protozoa. The hierarchical fractal dimensions values for prokaryotic kingdoms are lower than for other kingdoms. The Dr value for Viruses was lower than most eukaryotic kingdoms, but greater than prokaryotes. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with large subtaxa size. The proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the distribution of subtaxa in taxa can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. Our study determined the fractal dimensions for inter- and intra-taxonomic levels of the present tree of life. These results emphases the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups and skewness of taxa with large subtaxa size.

scholarly journals The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Xiaofei Lv ◽  
Yuping Wu ◽  
Bin Ma
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Dimensions ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life display a consistent power-law rules for inter- and intra-taxonomic levels, but the fractal dimensions were different among different kingdoms. The fractal dimension of hierarchical structure (Dr) is 0.873 for the entire tree of life, which smaller than the values of Dr for Animalia and Plantae but greater than the values of Dr for Fungi, Chromista, and Protozoa. The hierarchical fractal dimensions values for prokaryotic kingdoms are lower than for other kingdoms. The Dr value for Viruses was lower than most eukaryotic kingdoms, but greater than prokaryotes. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with large subtaxa size. The proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the distribution of subtaxa in taxa can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. Our study determined the fractal dimensions for inter- and intra-taxonomic levels of the present tree of life. These results emphases the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups and skewness of taxa with large subtaxa size.

scholarly journals MHD-waves in the geomagnetic tail: A review

10.12737/7168 ◽  
2015 ◽  
Vol 1 (1) ◽  
pp. 4-22 ◽  
Author(s):  
Анатолий Леонович ◽  
Anatoliy Leonovich ◽  
Виталий Мазур ◽  
Vitaliy Mazur ◽  
Даниил Козлов ◽  
...  
Keyword(s):  
Numerical Models ◽  
Experimental Studies ◽  
Low Frequency ◽  
Detailed Comparison ◽  
Mhd Waves ◽  
Theoretical Studies ◽  
Geomagnetic Tail ◽  
Magnetopause Oscillations ◽  
Experimental And Theoretical Studies ◽  
Theoretical Results

This article presents the review of experimental and theoretical studies on ultra-low-frequency MHD oscillations of the geomagnetic tail. We consider the Kelvin–Helmholtz instability at the magnetopause, oscillations with a discrete spectrum in the “magic frequencies” range, the ballooning instability of coupled Alfvén and slow magnetosonic waves, and “flapping” oscillations of the current sheet of the geomagnetic tail. Over the last decade, observations from THEMIS, CLUSTER and Double Star satellites have been of great importance for experimental studies. The use of several spacecraft allows us to study the structure of MHD oscillations with high spatial resolution. Due to this, we can make a detailed comparison between theoretical results and those obtained from multi-spacecraft studies. To make such comparisons in theoretical studies, in turn, we have to use the numerical models closest to the real magnetosphere.

EFFECT OF BARIUM ON DIELECTRIC, FERROELECTRIC, IMPEDANCE AND ELECTRICAL MODULUS PROPERTIES OF Bi0.5Na0.5TiO3 CERAMICS

2011 ◽  
Vol 25 (22) ◽  
pp. 2931-2948 ◽  
Author(s):  
K. SAMBASIVA RAO ◽  
K. CH. VARADA RAJULU ◽  
B. TILAK
Keyword(s):  
Power Law ◽  
Single Phase ◽  
Low Frequency ◽  
Rhombohedral Structure ◽  
Conductivity Spectrum ◽  
X Ray ◽  
Impedance Spectroscopy Study ◽  
Conventional Sintering ◽  
Phase Compound ◽  
Jonscher’S Power Law

Perovskite structured ferroelectric ( Na 1/2 Bi 1/2)0.945 Ba 0.055 TiO 3 (BNBT-5.5) material has been synthesized by the conventional sintering technique. X-ray analysis on the material showed a single phase compound with rhombohedral structure with lattice parameters a = 3.89 Åand α = 89.893 Å. Frequency and temperature dependence of dielectric permittivity, impedance, modulus and conductivity have been performed in the frequency and temperature range 45 Hz–5 MHz and 35–595°C, respectively. The observed low frequency dielectric dispersion (LFDD) in the material could be explained by Jonschers power law and evaluated activation energies at different temperature regions. Impedance spectroscopy study showed the presence of both bulk and grain boundary effects in the materials. The ac conductivity spectrum obeyed the Jonscher's power law. Modulus analysis indicated the possibility of hopping mechanism for electrical process in the system.

scholarly journals Spectral Index Versus Frequency and Models for the Continua of AGN and QSOs

1989 ◽  
Vol 134 ◽  
pp. 201-202
Author(s):  
Wayne A. Stein
Keyword(s):  
Accretion Disk ◽  
Spectral Index ◽  
Power Law ◽  
Spectral Distribution ◽  
Secondary Electron ◽  
Low Frequency ◽  
Spectral Indices ◽  
Ultraviolet Continuum ◽  
Electron Synchrotron ◽  
X Ray

The observed spectral index as a function of frequency of QSO continua must be explained in models. It is generally increasing (F(ν) ∝ ν−α, α increasing) with higher frequency in the infrared (downward curvature). The visual to ultraviolet continuum has been shown to be a broken power law with F(ν) ∝ ν−0.5 at low frequency and a break to larger α at νo ∼ 3×1015 Hz. X-ray observations frequently exhibit a flat continuum with α < 1. One prominent example is 3C273 for which α1–3μm → 2, αvis ∼ 0.5 and αx ∼ 0.5. These spectral indices arise naturally in Secondary Electron Synchrotron Self-Compton (SESSC) models. Some accretion disk models approach these spectral indices for the visual-ultraviolet portion of the spectral distribution.

GROWTH OF COLLOIDAL CRYSTALS UNDER MICROGRAVITY

2002 ◽  
Vol 16 (01n02) ◽  
pp. 338-345 ◽  
Author(s):  
M. ISHIKAWA ◽  
H. MORIMOTO ◽  
T. OKUBO ◽  
T. MAEKAWA
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Brownian Dynamics ◽  
Normal Gravity ◽  
Colloidal Crystals ◽  
Growth Dynamics ◽  
Sounding Rocket ◽  
Microgravity Experiment ◽  
Colloidal Crystallization ◽  
Number Of Particles

The growth dynamics of colloidal crystallization was evaluated under sedimentation free conditions using sounding rocket and Brownian Dynamics (BD) simulation. The Bragg's reflections of colloidal crystals were measured during microgravity flight and average sizes of crystallites were obtained by the Sherrer's method. Results showed a power-law relationship between size and time, L ∝ tα where L is the size of crystallites and t is time. The obtained α s were 0.33 ± 0.03 in microgravity and 0.25 ± 0.02 in normal gravity, respectively. Browninan Dynamics (BD) simulation showed the time evolution of ordered domains that consisted of connected structures of crystalline clusters. The power law relationship n ∝ t0.5 in post-nucleation period was confirmed between the number of particles (n) in clusters and time. The calculated power was related to α using the fractal dimension of crystalline clusters and α = 0.31 was obtained. The value was matched well with that of the microgravity experiment.

scholarly journals Study of spider pulsar binary eclipses and discovery of an eclipse mechanism transition

2020 ◽  
Vol 494 (2) ◽  
pp. 2948-2968 ◽  
Author(s):  
E J Polzin ◽  
R P Breton ◽  
B Bhattacharyya ◽  
D Scholte ◽  
C Sobey ◽  
...  
Keyword(s):  
Direct Evidence ◽  
Low Frequency ◽  
Line Of Sight ◽  
Observational Constraints ◽  
Main Body ◽  
Theoretical Studies ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Mechanism Transition ◽  
Hubble Time

ABSTRACT We present a comparative study of the low-frequency eclipses of spider (compact and irradiating binary) PSRs B1957+20 and J1816+4510. Combining these data with those of three other eclipsing systems we study the frequency dependence of the eclipse duration. PSRs B1957+20 and J1816+4510 have similar orbital properties, but the companions to the pulsars have masses that differ by an order of magnitude. A dedicated campaign to simultaneously observe the pulsed and imaged continuum flux densities throughout the eclipses reveals many similarities between the excess material within the two binaries, irrespective of the companion star properties. The observations show that the pulsar fluxes are removed from the line of sight throughout the main body of the eclipses. For PSR J1816 + 4510, we present the first direct evidence of an eclipse mechanism that transitions from one that removes the pulsar flux from the line of sight to one that merely smears out pulsations, and claim that this is a consequence of scattering in a tail of material flowing behind the companion. Inferred mass-loss rates from the companion stars are found to be $\dot{M}_{\text{C}} \sim 10^{-12}$ and $\sim 2 \times 10^{-13}\,\mathrm{M}_\odot$ yr−1 for PSR B1957+20 and PSR J1816 + 4510, respectively; seemingly too low to evaporate the stars within Hubble time. Measurements of eclipse durations over a wide range of radio frequencies show a significant dependence of eclipse duration on frequency for all pulsars, with wider eclipses at lower frequencies. These results provide a marked improvement in the observational constraints available for theoretical studies of the eclipse mechanisms.

scholarly journals Dielectric Constants of a Binary Solution Near the Critical Solution Temperature

1973 ◽  
Vol 51 (4) ◽  
pp. 545-550 ◽  
Author(s):  
I. Lubezky ◽  
R. McIntosh
Keyword(s):  
High Frequency ◽  
Binary Solution ◽  
Critical Concentration ◽  
Low Frequency ◽  
Dielectric Constants ◽  
Solution Temperature ◽  
Dielectric Losses ◽  
Theoretical Studies ◽  
Critical Solution Temperature ◽  
Experimental Knowledge

The dielectric constants and dielectric losses of solutions of nitrobenzene and 2,2,4-trimethyl pentane have been measured near the critical solution temperature over a concentration range of 22–75% by weight and in the frequency regions of 5–60 and 1000 – 4000 kHz. It was found that below a critical concentration of 35% maxima existed in ε′ and ε″ at a temperature of 0.3 °C above the critical solution temperature. At higher concentrations the maxima disappeared and phase separation was preceded only by changes in the thermal coefficients dε′/dT and dε″/dT. The present study combined with others indicates that two regions of loss exist for the system near the critical temperature: low frequency losses of a conductive nature and high frequency losses of the Debye type. The published experimental knowledge of such systems remains insufficient to enable a thorough test of the theoretical studies published recently by Snider.

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