arXiv subjects

Jiang Zhang

Publications and source records attributed to Jiang Zhang.

100 records · Page 6Linked to original sources

arXiv2011

Accelerating Growth and Size-dependent Distribution of Human Activities Online

Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^γ(γ=1)$. However, we find examples of systems where total activity grows faster than active population. Our study shows that the power law relationship $T\propto P^γ(γ>1)$ is in fact ubiquitous in online activities such as micro-blogging, news voting and photo tagging. We call the pattern "accelerating growth" and find it relates to a type of distribution that changes with system size. We show both analytically and empirically how the growth rate $γ$ associates with a scaling parameter $b$ in the size-dependent distribution. As most previous studies explain accelerating growth by power law distribution, the model of size-dependent distribution is novel and worth further exploration.

physics.soc-ph↗

arXiv2011

The "S" Curve Relationship between Export Diversity and Economic Size of Countries

The highly detailed international trade data among all countries in the world during 1971-2000 shows that the kinds of export goods and the logarithmic GDP (gross domestic production) of a country has an S-shaped relationship. This indicates all countries can be divided into three stages accordingly. First, the poor countries always export very few kinds of products as we expect. Second, once the economic size (GDP) of a country is beyond a threshold, its export diversity may increase dramatically. However, this is not the case for rich countries because a ceiling on the export diversity is observed when their GDPs are higher than another threshold. This pattern is very stable for different years although the concrete parameters of the fitting sigmoid functions may change with time. In addition, we also discussed other relationships such as import diversity with respect to logarithmic GDP, diversity of exporters with respect to the number of export goods etc., all of these relationships show S-shaped or power law patterns. Although this paper does not explain the origin of the S-shaped curve, it may provide a basic empirical fact and insights for economic diversity.

q-fin.GN↗

arXiv2011

Size-Dependency of Income Distributions and Its Implications

This paper highlights the size-dependency of income distributions, i.e. the income distribution curves versus the population of a country systematically. By using the generalized Lotka-Volterra model to fit the empirical income data in the United States during 1996-2007, we found an important parameter $λ$ can scale with a $β$ power of the size (population) of U.S. in that year. We pointed out that the size-dependency of the income distributions, which is a very important property but seldom addressed by previous studies, has two non-trivial implications: (1) the allometric growth pattern, i.e. the power law relationship between population and GDP in different years, which can be mathematically derived from the size-dependent income distributions and also supported by the empirical data; (2) the connection with the anomalous scaling for the probability density function in critical phenomena since the re-scaled form of the income distributions has the exactly same mathematical expression for the limit distribution of the sum of many correlated random variables asymptotically.

q-fin.GN↗

arXiv2011

Exact Solution for Optimal Navigation with Total Cost Restriction

Recently, Li \textit{et al.} have concentrated on Kleinberg's navigation model with a certain total length constraint $Λ= cN$, where $N$ is the number of total nodes and $c$ is a constant. Their simulation results for the 1- and 2-dimensional cases indicate that the optimal choice for adding extra long-range connections between any two sites seems to be $α=d+1$, where $d$ is the dimension of the lattice and $α$ is the power-law exponent. In this paper, we prove analytically that for the 1-dimensional large networks, the optimal power-law exponent is $α=2$ Further, we study the impact of the network size and provide exact solutions for time cost as a function of the power-law exponent $α$. We also show that our analytical results are in excellent agreement with simulations.

physics.soc-ph↗

arXiv2010

Study of isotopic fractions and abundances of the neutron-capture elements in HD 175305

The chemical abundances of metal-poor stars are excellent sources of information for setting new constraints on models of Galactic chemical evolution at low metallicities. In this paper we present an attempt to fit the elemental abundances observed in the bright, metal-poor giant HD 175305, and derive isotopic fractions using a parametric model. The observed abundances can be wellmatched by the combined contributions froms- and r-processmaterial. The component coefficients of the r- and s-processes are C1 = 3.220 and C3 = 1.134, respectively. The Smisotopic fraction in this star where the observed neutron-capture elements are produced is predicted to be f 152+154 =0.582,which suggests that, even though the r-process is predominantly responsible for the synthesis of the neutron-capture elements in the early Galaxy, the onset of the s-process had already occurred at this metallicity of [Fe/H] = -1.6.

astro-ph.SR↗

arXiv2010

A holistic abundance analysis of r-rich stars

The chemical abundances of metal-poor stars are an excellent test bed by which to set new constraints on models of neutron-capture processes at low metallicity. Some r-process-rich (hereafter r-rich) metal-poor stars, such as HD221170, show an overabundance of the heavier neutron-capture elements and excesses of lighter neutron-capture elements. The study of these r-rich stars could give us a better understanding of weak and main r-process nucleosynthesis at low metallicity. Based on conclusions from the observation of metal-poor stars and neutron-capture element nucleosynthesis theory, we set up a model to determine the relative contributions from weak and main r-processes to the heavy-element abundances in metal-poor stars. Using this model, we find that the abundance patterns of light elements for most sample stars are close to the pattern of weak r-process stars, and those of heavier neutron-capture elements very similar to the pattern of main r-process stars, while the lighter neutron-capture elements can be fitted by the mixing of weak and main r-process material. The production of weak r-process elements appears to be associated with the light elements, while the production of main r-process elements is almost decoupled from that of the light elements. We compare our results with the observed data at low metallicities, showing that the predicted trends are in good agreement with the observed trends, at least for the metallicity range [Fe/H] < -2.1. For most sample stars, the abundance patterns of both neutron-capture elements and light elements could be best explained by a star formed in a molecular cloud that has been polluted by both weak and main r-process material.

astro-ph.SR↗

arXiv2010

Investigation for the enrichment pattern of the element abundances in r+s star HE 0338-3945: a special r-II star?

The very metal-poor star HE 0338-3945 shows a double-enhanced pattern of the neutron-capture elements. The study to this sample could make people gain a better understanding of s- and r-process nucleosynthesis at low metallicity. Using a parametric model,we find that the abundance pattern of the neutron-capture elements could be best explained by a binary system formed in a molecular cloud, which had been polluted by r-process material. The observed abundance pattern of C and N can be explained by an AGB model(Karakas & Lattanzio 2007), . Combing with the parameters obtained from Cui & Zhang (2006), we suggest that the initial mass of the AGB companion is most likely to be about 2.5Msun, which excludes the possibility of forming a type-1.5 supernova. By comparing with the observational abundance pattern of CS 22892-052, we find that the dominating production of O should accompany with the production of the heavy r-process elements of r+s stars. Similar to r-II stars, the heavy r-process elements are not produced in conjunction with all the light elements from Na to Fe group. The abundance pattern of the light and r-process elements for HE 0338-3945 is very close to the pattern of the r-II star CS 22892-052. So, we suggest that this star HE 0338-3945 should be a special r-II star.

astro-ph.SR↗

arXiv2010

Allometric Scaling of Countries

As huge complex systems consisting of geographic regions, natural resources, people and economic entities, countries follow the allometric scaling law which is ubiquitous in ecological, urban systems. We systematically investigated the allometric scaling relationships between a large number of macroscopic properties and geographic (area), demographic (population) and economic (GDP, gross domestic production) sizes of countries respectively. We found that most of the economic, trade, energy consumption, communication related properties have significant super-linear (the exponent is larger than 1) or nearly linear allometric scaling relations with GDP. Meanwhile, the geographic (arable area, natural resources, etc.), demographic(labor force, military age population, etc.) and transportation-related properties (road length, airports) have significant and sub-linear (the exponent is smaller than 1) allometric scaling relations with area. Several differences of power law relations with respect to population between countries and cities were pointed out. Firstly, population increases sub-linearly with area in countries. Secondly, GDP increases linearly in countries but not super-linearly as in cities. Finally, electricity or oil consumptions per capita increases with population faster than cities.

physics.soc-ph↗

arXiv2010

Scaling Behaviors of Weighted Food Webs as Energy Transportation Networks

Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous scaling behaviors. Two random variables $A_i$ and $C_i$ defined for each vertex $i$, representing the total flux (also called vertex intensity) and total indirect effect or energy store of $i$, were found to follow power law distributions with the exponents $α\approx 1.32$ and $β\approx 1.33$, respectively. Another scaling behavior is the power law relationship, $C_i\sim A_i^η$, where $η\approx 1.02$. This is known as the allometric scaling power law relationship because $A_i$ can be treated as metabolism and $C_i$ as the body mass of the sub-network rooted from the vertex $i$, according to the algorithm presented in this paper. Finally, a simple relationship among these power law exponents, $η=(α-1)/(β-1)$, was mathematically derived and tested by the empirical food webs.

physics.bio-ph↗

arXiv2006

The yields of r-process elements and chemical evolution of the Galaxy

The supernova yields of r-process elements are obtained as a function of the mass of their progenitor stars from the abundance patterns of extremely metal-poor stars on the left-side [Ba/Mg]-[Mg/H] boundary with a procedure proposed by Tsujimoto and Shigeyama. The ejected masses of r-process elements associated with stars of progenitor mass $M_{ms}\leq18M_{\odot}$ are infertile sources and the SNe II with 20$M_{\odot}\leq M_{ms}\leq 40M_{\odot}$are the dominant source of r-process nucleosynthesis in the Galaxy. The ratio of these stars 20$M_{\odot}\leq M_{ms}\leq40M_{\odot}$ with compared to the all massive stars is about $\sim$18%. In this paper, we present a simple model that describes a star's [r/Fe] in terms of the nucleosynthesis yields of r-process elements and the number of SN II explosions. Combined the r-process yields obtained by our procedure with the scatter model of the Galactic halo, the observed abundance patterns of the metal-poor stars can be well reproduced

astro-ph↗