Percolation and universality

Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson

Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. A cluster recognition algorithm is developed to obtain properties of percolation models. The fractal nature of a percolating system is discussed, along with general features of fractals. Scaling laws and critical exponents, which are central features of modern approaches to complex systems, are also introduced and illustrated with percolating systems. The important concept of a correlation function is also used to characterize these systems. Finally, the insensitivity of large classes of model systems with respect to short range dynamics, known as universality, is discussed in the context of percolation. This is illustrated with the modern concepts of coarse graining and the renormalization group.

2003 ◽  
Vol 17 (16) ◽  
pp. 885-896 ◽  
Author(s):  
Su-Long Nyeo ◽  
I-Ching Yang

The phase transition of DNA molecules is studied in an exactly solvable formalism with the Morse and Deng–Fan potentials for the interstrand hydrogen bonds of nucleotide base pairs. It is shown that although the two potentials have different short-range behaviors, the thermodynamic quantities of the DNA system in these potentials enjoy the same scaling laws with the associated critical exponents, which are explicitly calculated. These exactly solvable DNA models are shown to exhibit a phase transition of the second order and the results of the analysis agree with previous studies.


1995 ◽  
Vol 269 (2) ◽  
pp. H480-H486 ◽  
Author(s):  
Y. Yamamoto ◽  
J. O. Fortrat ◽  
R. L. Hughson

The purpose of the present study was to investigate the basic fractal nature of the variability in resting heart rate (HRV), relative to that in breathing frequency (BFV) and tidal volume (TVV), and to test the hypothesis that fractal HRV is due to the fractal BFV and/or TVV in humans. In addition, the possible fractal nature of respiratory volume curves (RVC) and HRV was observed. In the first study, eight subjects were tested while they sat quietly in a comfortable chair for 60 min. Beat-to-beat R-R intervals, i.e., HRV, and breath-by-breath BFV and TVV were measured. In the second study, six subjects were tested while they were in the supine position for 20-30 min. The RVC was monitored continuously together with HRV. Coarse-graining spectral analysis (Yamamoto, Y., and R. L. Hughson, Physica D 68: 250-264, 1993) was applied to these signals to evaluate the percentage of random fractal components in the time series (%Fractal) and the spectral exponent (beta), which characterizes irregularity of the signals. The estimates of beta were determined for each variable only over the range normally used to evaluate HRV. Values for %Fractal and beta of both BFV and TVV were significantly (P < 0.05) greater than those for HRV. In addition, there was no significant (P > 0.05) correlation between the beta values of HRV relative to either BFV (r = 0.14) or TVV (r = 0.34). RVC showed a smooth oscillation as compared with HRV; %Fractal for RVC (42.3 +/- 21.7%, mean +/- SD) was significantly (P < 0.05) lower than that for HRV (78.5 +/- 4.2%).(ABSTRACT TRUNCATED AT 250 WORDS)


2019 ◽  
Vol 21 (27) ◽  
pp. 14873-14878 ◽  
Author(s):  
Pietro Corsi ◽  
Elia Roma ◽  
Tecla Gasperi ◽  
Fabio Bruni ◽  
Barbara Capone

Scaling multiscale approach to coarse grain bottle brushes polymeric macromolecules as effective chains of tethered star polymers.


2009 ◽  
pp. 1135-1142
Author(s):  
Victor I. Khashchanskiy ◽  
Andrei L. Kustov

One of the applications of m-commerce is mobile authorization, that is, rights distribution to mobile users by sending authorization data (a token) to the mobile devices. For example, a supermarket can distribute personalized discount coupon tokens to its customers via SMS. The token can be a symbol string that the customers will present while paying for the goods at the cash desk. The example can be elaborated further—using location information from the mobile operator, the coupons can only be sent to, for example, those customers who are in close vicinity of the mall on Saturday (this will of course require customers to allow disclosing their location). In the example above, the token is used through its manual presentation. However, most interesting is the case when the service is released automatically, without a need for a human operator validating the token and releasing a service to the customer; for example, a vending machine at the automatic gas station must work automatically to be commercially viable. To succeed, this approach requires a convenient and uniform way of delivering authorization information to the point of service—it is obvious that an average user will only have enough patience for very simple operations. And this presents a problem. There are basically only three available local (i.e., short-range) wireless interfaces (LWI): WLAN, IR, and Bluetooth, which do not cover the whole range of mobile devices. WLAN has not gained popularity yet, while IR is gradually disappearing. Bluetooth is the most frequently used of them, but still it is not available in all phones. For every particular device it is possible to send a token out using some combination of LWI and presentation technology, but there is no common and easy-to-use combination. This is a threshold for the development of services. Taking a deeper look at the mobile devices, we can find one more non-standard simplex LWI, which is present in all devices—acoustical, where the transmitter is a phone ringer. Token presentation through acoustic interface along with general solution of token delivery via SIM Toolkit technology (see 3GPP TS, 1999) was presented by Khashchanskiy and Kustov (2001). However, mobile operators have not taken SIM Toolkit into any serious use, and the only alternative way of delivering sound tokens into the phone-ringing tone customization technology was not available for a broad range of devices at the time the aforementioned paper was published. Quite unexpectedly, recent development of mobile phone technologies gives a chance for sound tokens to become a better solution for the aforementioned problem, compared with other LWI. Namely, it can be stated that every contemporary mobile device supports either remote customization of ringing tones, or MMS, and in the majority of cases, even both, thus facilitating sound token receiving over the air. Most phone models can playback a received token with only a few button-clicks. Thus, a sound token-based solution meets the set criteria better than any other LWI. Token delivery works the same way for virtually all phones, and token presentation is simple. In this article we study the sound token solution practical implementation in detail. First, we select optimal modulation, encoding, and recognition algorithm, and we estimate data rate. Then we present results of experimental verification.


2018 ◽  
Vol 30 (5) ◽  
pp. 853-868
Author(s):  
CHRISTIAN KUEHN ◽  
FRANCESCO ROMANO

Critical transitions (or tipping points) are drastic sudden changes observed in many dynamical systems. Large classes of critical transitions are associated with systems, which drift slowly towards a bifurcation point. In the context of stochastic ordinary differential equations, there are results on growth of variance and autocorrelation before a transition, which can be used as possible warning signs in applications. A similar theory has recently been developed in the simplest setting for stochastic partial differential equations (SPDEs) for self-adjoint operators in the drift term. This setting leads to real discrete spectrum and growth of the covariance operator via a certain scaling law. In this paper, we develop this theory substantially further. We cover the cases of complex eigenvalues, degenerate eigenvalues as well as continuous spectrum. This provides a fairly comprehensive theory for most practical applications of warning signs for SPDE bifurcations.


2010 ◽  
Vol 132 (9) ◽  
pp. 091101 ◽  
Author(s):  
Andreas S. Poulos ◽  
Doru Constantin ◽  
Patrick Davidson ◽  
Brigitte Pansu ◽  
Éric Freyssingeas ◽  
...  

2006 ◽  
Vol 61 (5-6) ◽  
pp. 239-248 ◽  
Author(s):  
Kazuhiro Matsumoto ◽  
Hans H. Diebner

We introduce a simple method for nonlinear parameter estimation based on a structural comparison of target and model attractor. The parameters of the model are adapted by means of minimizing the structural difference of the attractors. For this quantitative comparison histograms derived from a coarse graining of the phase spaces are used. We present a time discrete as well as a continuous example to demonstrate the efficiency of this method. The target attractors are computed from the Hénon map and the Rössler system, respectively. The model systems are chosen to be fairly universal endowed with free parameters that are adapted so that the model attractor resembles the target. The estimations work accurate and acceptably fast up to four parameters


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