Fractal Concepts in Condensed Matter Physics by Professor Tsuneyoshi Nakayama, Professor Kousuke Yakubo

By Professor Tsuneyoshi Nakayama, Professor Kousuke Yakubo (auth.)

Concisely and obviously written, this e-book presents a self-contained creation to the elemental strategies of fractals and demonstrates their use in a variety of issues in condensed topic physics and statistical mechanics. the 1st half outlines various fractal constructions saw in condensed topic. the most a part of the booklet is devoted to the dynamical behaviour of fractal constructions, together with anomalous and percolating structures. the concept that of multifractals is illustrated for the metal-insulator quantum part transition. The authors emphasizes the unified description of those assorted dynamic difficulties, therefore making the e-book available to readers who're new to the field.

Show description

Read Online or Download Fractal Concepts in Condensed Matter Physics PDF

Similar physics books

Introduction to the Physics of Waves

Balancing concise mathematical research with the real-world examples and sensible functions that motivate scholars, this textbook presents a transparent and approachable creation to the physics of waves. the writer exhibits via a wide strategy how wave phenomena will be saw in numerous actual events and explains how their features are associated with particular actual principles, from Maxwell's equations to Newton's legislation of movement.

Philosophy, Mathematics and Modern Physics: A Dialogue

In recent years a brand new discussion has began among the average sciences and the arts. this can be fairly real of physics and philosophy, whose sphere of mutual curiosity multiplied considerably with the appearance of quantum mechanics. between different themes, the dialogue covers the evolution of theories, the function of arithmetic within the actual sciences, the conception and cognition of nature and definitions of house and time.

Molecular Physics and Hypersonic Flows

Molecular Physics and Hypersonic Flows bridges the space among the fluid dynamics and molecular physics groups, emphasizing the position performed through undemanding strategies in hypersonic flows. specifically, the paintings is basically devoted to filling the distance among microscopic and macroscopic remedies of the resource phrases to be inserted within the fluid dynamics codes.

Additional resources for Fractal Concepts in Condensed Matter Physics

Example text

This assumption provides a basis for the scaling ansatz which will be presented later in this section. The difference between second-order thermodynamic phase transitions and percolation transitions is that decreasing temperature T corresponds to increasing p. 1) is called the correlation length exponent. For an infinite cluster obtained at p = Pc, the characteristic length scale ~ of the system diverges, indicating that the length scale vanishes in the system. , a scale-invariant system. There are two kinds of percolating networks: site percolating and bond percolating.

In many cases of statistically distributed measures, the number of boxes possessing the smallest or the largest box measure is unity, which does not depend on L or l. This means that f -00 and f 00 vanish. Next we consider the case of q = O. Lb(l) ::f. Lb(l) is proportional to [-Df, where Df is the fractal dimension of the support. 78) and Do = Df. 79) 52 4. 80) z(O) = 0, and dz(q) I dq q=O = 2a(q)l q=o - 2a(2q)l q =o = O. 81) Since z(q) is always positive, z(q) takes the minimum value z(O) = 0 at q = O.

Voltage drops in the second generation of the hierarchical resistor network (HRN) model across which a unit voltage is applied. We define the resistance of a single bond to be unity. Fractional numbers indicate voltage drops between both ends of bonds 38 4. Multifractals and (k=O,I, ... ,n). 11) We should note that the q th moment of the distributed quantities V is dominated by larger or smaller values of V if q » 1 or q « -1, respectively. 13) The exponent ~o = 2 j v is the fractal dimension of the 0 th moment.

Download PDF sample

Rated 4.38 of 5 – based on 14 votes