中文簡介

在過去的幾十年里，涉及復(fù)雜幾何、模式和尺度的現(xiàn)象研究經(jīng)歷了驚人的發(fā)展。在這相對較短的時間內(nèi)，幾何和/或時間尺度已經(jīng)被證明代表了在物理、數(shù)學(xué)、生物學(xué)、化學(xué)、經(jīng)濟(jì)學(xué)、技術(shù)和人類行為等不同尋常的領(lǐng)域中發(fā)生的許多過程的共同方面。通常，一個現(xiàn)象的復(fù)雜性表現(xiàn)在其底層復(fù)雜的幾何結(jié)構(gòu)中，在大多數(shù)情況下可以用具有非整數(shù)(分形)維數(shù)的對象來描述。在其他情況下，事件在時間上的分布或各種其他數(shù)量的分布顯示特定的縮放行為，從而更好地理解決定給定流程的相關(guān)因素。在相關(guān)的理論、數(shù)值和實驗研究中，將分形幾何和尺度作為一種語言，使我們能夠更深入地了解以前難以解決的問題。其中，通過應(yīng)用尺度不變性、自親和性和多分形性等概念，對增長現(xiàn)象、湍流、迭代函數(shù)、膠體聚集、生物模式形成、股票市場和非均勻材料有了更好的理解。專門研究上述現(xiàn)象的期刊的主要挑戰(zhàn)在于其跨學(xué)科的性質(zhì);我們致力于匯集這些領(lǐng)域的最新發(fā)展，以便就自然界和社會中復(fù)雜的時空行為采取各種方法和科學(xué)觀點進(jìn)行富有成效的相互作用。

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英文簡介

The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, technology and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.