scaling laws 中文意思是什麼
scaling laws
解釋
比例法則-
The use of the state - of - the - art laser facility makes it possible to create conditions of the same or similar to those in the astrophysical processes. the introduction of the astrophysics - relevant ideas in laser - plasma experiments is propitio us to the understanding of the astrophysical phenomena. however, the great difference between the laser - produced plasmas and the astrophysical processes makes it awkward to model the latter by laser - plasma experiments. this paper addresses the physical backgrounds for modeling the astrophysical plasmas by laser plasmas, connecting these two kinds of plasmas by scaling laws. thus, allowing the creation of experimental test beds where observations and models can be quantitatively compared with laser - plasma data. special attentions are paid on the possibilities of using home - made laser facilities to model astrophysical phenomena
採用當前最先進的激光裝置與物質相互作用，可以獲得與天體物理過程中相同或相似的條件，並進而開展利用激光等離子體模擬天體物理現象的實驗.然而，激光等離子體為微米空間尺度、納秒存活時間，而天體物理對象則為宇宙學的極大的時間與空間尺度，對在物理上和實際操作上將這兩種表面上存在巨大差異的物理過程對應起來從而利用激光等離子體研究天體物理過程的可能性進行了討論，特別是對利用國內的激光裝置開展模擬實驗的可行性進行了討論 -
The mechanism of shock formation apparently changes, too, at these altitudes so that the scaling laws are no longer applicable.
在這個高度下，沖擊形成的機制也有很明顯的改變，所以遞增公式也就不再適用了。 -
Thus scale - measurement - dimension constitutes the fundamental concepts of this project. the scaling laws are derived from different perspectives, using entropy - maximizing methods in macro - level and utility - maximizing method in micro - level, consequently a pair of dual models based on the idea from nonlinear programming are built to interpret both the scaling laws and thus power laws. a discovery is that the energy and information can be transformed into each other in urban systems
藉助熵最大化方法從宏觀上推導了標度律，利用效用最大化原理從微觀上導出了標度律，然後建設了熵與效用最大化的對偶轉換模型;通過對簡單的網路模型的研究，論證熵與效用最大化過程本質上是追求系統整體上的最高效率與局部公平合理。 -
All the contents are developed around a set of scaling laws taking the form of exponentials which relate to almost all the issues of complexity including fractals, chaos, strange attractors, localization, and symmetry breaking, etc. the main work can be summarized as follows : starting from the law of allmetric growth three fractal dimensions in a broad sense are derived, and according to these dimensions, geographical space is divided into three levels, i. e., real space, phase space, and order space, each of which corresponds to a kind of dimension. based on the idea of spatial disaggregation and using the rmi ( relationship - mapping - reversion ) principle, the urban system is formulated as three scaling laws of the three spaces, including number law, size law, and area law, which can be transformed into a set of power laws such as allometric law and zipf ’ s law associated with fractal structure
從異速生長律的縱向、橫向和切向三個角度將地理空間劃分為實空間、相空間和序空間，分別對應于空間系列、時間序列和等級序列三個層面，每個層面的測度各有自己的空間維度。基於「空間循環細分-等級體系-網路結構」的數理等價關系，利用rmi （關系-映射-反演）原則，成功地實現了城市系統宏觀模型的理論抽象，將空間復雜性問題表徵為簡單的指數式標度定律（包括數量律、規模律和尺度律） ，這一組標度律可以與一組冪次定律（包括具有分形性質的規模-數目律、異速生長定律和三參數zipf定律）互為變換。 -
The braess paradox model is taken as an example to reveal the essence of entropy - maximization and utility - maximization which lies in the unity of the most efficient for the whole and the fairest for local parts and individuals. the internal symmetry of the scaling laws are bring to light based on the dual model of entropy - and utility - maximization. the internal symmetry including translational symmetry, dilation symmetry, and bilateral symmetry originate from relative energy - conservation and information conservation of urban systems reflected by the dual models, and parity conservation of scaling laws
揭示標度律及其等價模型各種對稱性質，發現城市系統具有平移對稱、鏡像對稱和標度對稱等內部對稱性，這些對稱性都對應著城市系統的不可觀測量，其本質在於系統內部隱含的守恆律，包括標度變換的奇偶守恆、能量和信息的相對守恆等。 -
In the field of polymer solutions, a series of high precision measurements of the critical properties of polymer solutions near their critical points by his group has established scaling laws and resolved several long - standing disputes about the exact values of the associated exponents and the relations among them. the results are now benchmark data sets against which various theoretical models are tested
在聚合物溶液的研究領域中，他領導的研究小組完成了一系列有關聚合物在臨界點附近的高精度測量。這些工作導致了一系列標度律的建立並且結束了對有關標度指數數值的長期爭論。這些實驗結果現已成為驗證多種理論模型的基準資料。 -
If sociological laws determine the degree of anything, they will do so only in very vague terms, and will permit, at the best, a very rough scaling.
如果社會學的規律能夠確定任何事情的程度，它們也只能用十分含糊的措詞，充其量只能作出大致的估計。
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