By Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera
Networks delivers an invaluable version and image photograph precious for the outline of a wide number of web-like buildings within the actual and man-made realms, e.g. protein networks, meals webs and the web. The contributions accumulated within the current quantity offer either an creation to, and an outline of, the multifaceted phenomenology of complicated networks. Statistical Mechanics of advanced Networks also provides a cutting-edge photo of present theoretical equipment and techniques.
Read or Download Statistical Mechanics of Complex Networks (Lecture Notes in Physics) PDF
Similar system theory books
This ebook offers the mathematical foundations of platforms idea in a self-contained, complete, specific and mathematically rigorous method. this primary quantity is dedicated to the research of dynamical structures with emphasis on difficulties of uncertainty, while the second one quantity should be dedicated to regulate.
Al readers how Complexity--the watershed technological know-how schedule for no less than the nexttwo decades--is affecting our lives.
One criterion for classifying books is whether or not they're written for a unmarried function or for a number of reasons. This ebook belongs to the class of multipurpose books, yet considered one of its roles is predominant-it is essentially a textbook. As such, it may be used for numerous classes on the first-year graduate or upper-division undergraduate point.
Over the last years the sphere of synergetics has been mushrooming. An ever expanding variety of clinical papers are released at the topic, and diverse meetings worldwide are dedicated to it. looking on the actual features of synergetics being taken care of, those meetings could have such various titles as "Nonequilibrium Nonlinear Statistical Physics," "Self-Organization," "Chaos and Order," and others.
- Dynamical systems and applications
- Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine
- Coordination Control of Distributed Systems
- The essence of chaos
- Complexity: Metaphors, Models, and Reality
Additional info for Statistical Mechanics of Complex Networks (Lecture Notes in Physics)
Phys. 51, 1079 (2002). 2. H. Ernst: in Fractals in Physics, edited by L. Pietronero, E. Tosatti (Elsevier, Amsterdam, 1986), p. 289. 3. J. Bray: Adv. Phys. 43, 357 (1994). 4. A. Pimpinelli, J. Villain: Physics of Crystal Growth (Cambridge University Press, Cambridge, 1998). 5. A. A. Simon: Models of Man (Wiley, New York, 1957). 6. -L. Barab´ asi, R. Albert: Science 286, 509 (1999); R. Albert, H. -L. Barab´ asi: Nature 401, 130 (1999). 7. U. Yule: Phil. Trans. Roy. Soc. B 213, 21 (1924); The Statistical Study of Literary Vocabulary (Cambridge University Press, Cambridge, 1944).
U=1−q+ q k ∞ kP (k)uk−1 . 19) to calculate the size of the inﬁnite cluster in a graph with a given degree distribution. 3 Critical Exponents Using Abelian and Tauberian methods [25, 26] one can use . 20) to ﬁnd the critical exponents for percolation in scale free networks. Some preliminary results can be found in . A more detailed treatment can be found in [28, 19]. Here we just state the results. 21) 3 < λ < 4, 1 λ > 4. The number of clusters with size s behaves as ns ∼ (p − pc )−τ , where τ =2+ 1 2λ − 3 = , λ−2 λ−2 2<λ<4.
5 and λ = 5. Bottom: shown (in diﬀerent colors) are shells of equidistant sites to the central one in a lattice of 300 x 300 sites. 5, shells are broken dmin . We will see that dmin < 1 (for d > 1), contrary to all naturally occurring fractals and disordered media. Sites at chemical distance l from a given site constitute its l-th chemical shell. The number of (connected) sites within radius r scales as m(r) ∼ rdf , deﬁning the fractal dimension df . Likewise, the number of (connected) sites within chemical radius l scales as m(l) ∼ ldl , which deﬁnes the fractal dimension dl in chemical space.
Statistical Mechanics of Complex Networks (Lecture Notes in Physics) by Romualdo Pastor-Satorras, Miguel Rubi, Albert Diaz-Guilera