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Partner: UNT College of Arts and Sciences
Department: Center for Nonlinear Science
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Absorption and Emission in the Non-Poissonian Case
This article discusses absorption and emission in the Non-Poissonian Case. Abstract: This Letter addresses the challenging problems posed to the Kubo-Anderson (KA) theory by the discovery of intermittent resonant fluorescence with a nonexponential distribution of waiting times. We show how to extend the KA theory from aged to aging systems, aging for a very extended time period or even forever, being a crucial consequence of non-Poisson statistics. digital.library.unt.edu/ark:/67531/metadc67641/
Aging and Rejuvenation with Fractional Derivatives
This article discusses aging rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes a fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index μ in the interval 2<μ<3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, o, is given by o=3-μ. A brand new system is characterized by the degree o=μ-2. If the system is prepared at time -tₐ<0 and the observation begins at time t=0, we derive the following scenario. For times 0<t«tₐ the system is satisfactorily described by the fractional derivative with o=3-μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t⪢tₐ yields o=μ-2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc67638/
Aging and Rejuvenation with Fractional Derivatives
Paper discussing aging and rejuvenation with fractional derivatives. Abstract: We discuss a dynamic procedure that makes the fractional derivative emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index μ in the interval 2 < μ < 3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord = μ - 2. If the system is prepared at time -tₐ < 0 and the observation begins at time t = 0, we derive the following scenario. For times 0 < t << tₐ the system is satisfactorily described by the fractional derivative with ord = 3 - μ. Upon time increase the system undergoes a rejuvenation process that in the time limit t >> tₐ yields ord = μ - 2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative. digital.library.unt.edu/ark:/67531/metadc174699/
Aging in financial market
Article discussing aging in the financial market. Abstract: We analyze the data of the Italian and U.S. futures on the stock markets and we test the validity of the Continuous Time Random Walk assumption for the survival probability of the returns time series via a renewal aging experiment. We also study the survival probability of returns sign and apply a coarse graining procedure to reveal the renewal aspects of the process underlying its dynamics. digital.library.unt.edu/ark:/67531/metadc174703/
Anomalous diffusion and ballistic peaks: A quantum perspective
This article discusses anomalous diffusion and ballistic peaks. Abstract: The quantum kicked rotor and the classical kicked rotor are both shown to have truncated Lévy distributions in momentum space, when the classical phase space has accelerator modes embedded in a chaotic sea. The survival probability for classical particles at the interface of an accelerator mode and the chaotic sea has an inverse power-law structure, whereas that for quantum particles has a periodically modulated inverse power law, with the period of oscillation being dependent on Planck's constant. These logarithmic oscillations are a renormalization group property that disappears as ħ → 0 in agreement with the correspondence principle. digital.library.unt.edu/ark:/67531/metadc75417/
Anomalous diffusion and environment-induced quantum decoherence
This article discusses anomalous diffusion and environment-induced quantum decoherence. Abstract: We study the anomalous diffusion resulting from the standard map in the so-called accelerating state, and we observe that it is determined by unusually large times of sojourn of the classical trajectories in the fractal region at the border between the chaotic sea and the acceleration island. The quantum-mechanical breakdown of this property implies a coherence among so slightly different values of momentum as to become much more robust against environment fluctuations than the quantum localization corresponding to normal diffusion. digital.library.unt.edu/ark:/67531/metadc139477/
Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions
This article discusses anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation. Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence. digital.library.unt.edu/ark:/67531/metadc77162/
Beyond the Death of Linear Response: 1/f Optimal Information Transport
This article discusses linear response and 1/f optimal information transport. Article: Nonergodic renewal processes have recently been shown by several authors to be insensitive to periodic perturbations, thereby apparently sanctioning the death of linear response, a building block of nonequilibrium statistical physics. The authors show that it is possible to go beyond the "death of linear response" and establish a permanent correlation between an external stimulus and the response of a complex network generating nonergodic renewal processes, by taking as stimulus a similar nonergodic process. The ideal condition of 1/f noise corresponds to a singularity that is expected to be relevant in several experimental conditions. digital.library.unt.edu/ark:/67531/metadc40407/
This article is a reply to a comment by Massimo Falcioni and Angelo Vulpiani. In a previous letter, the authors have discussed the linear response theory (LRT) and shown that the breakdown of this theory occurring at intermediate times, observed in an earlier paper [2] as well as in [1], disappears upon an increase of the number of degrees of freedom. In a comment to [1] Falcioni and Vulpiani [3] claim that this breakdown is rather a consequence of the lack of mixing: according to them, regardless of the number of degrees of freedom, mixing is the key ingredient behind the LRT. digital.library.unt.edu/ark:/67531/metadc77166/
Brain, Music, and Non-Poisson Renewal Processes
Breakdown of the Onsager Principle as a Sign of Aging
Article discussing the breakdown of the Onsager principle as a sign of aging. Abstract: We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site or extended time. The sojourn times have a distribution ψ (t) that is assumed to be an inverse power law with the power index μ. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when ψ (t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. The case of Poissonian distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition hold true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless the nature of the waiting time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markovian. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light into the problem of how to unravel non-Markovian master equations. digital.library.unt.edu/ark:/67531/metadc174692/
Canonical and noncanonical equilibrium distribution
This article discusses canonical and noncanonical equilibrium distribution. Abstract: We address the problem of the dynamical foundation of noncanonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of noncanonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the noncanonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Lévy statistics are the best description of the dynamics and that the Lévy distribution is the correct basin of attraction. We show that the correct path to noncanonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics. digital.library.unt.edu/ark:/67531/metadc77164/
Chaos and thermal conductivity
This article discusses chaos and thermal conductivity. Abstract: We argue that the condition of local thermal equilibrium realized several years ago by Rich and Visscher [Phys. Rev. B 11, 2164 (1975)] through a process of mathematical convergence can be obtained dynamically by adopting the prescription of a recent paper [M. Bianucci, R. Mannella, B.J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)]. This should contribute to shedding light on the still unsolved problem fo the microscopic derivation of the heat Fourier law. digital.library.unt.edu/ark:/67531/metadc139502/
Cognitive Scale-Free Networks as a Model for Intermittency in Human Natural Language
Paper discussing cognitive scale-free networks as a model for intermittency in human natural language. Abstract: We model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. Using a time series approach, the diffusion entropy method (DE), we compute the complexity of an Italian corpus of newspapers and magazines. We find that the anomalous scaling index is compatible with a simple dynamical model, a random walk on a complex scale-free network, which is linguistically related to Saussurre's paradigms. The model yields the famous Zipf's law in terms of the generalized central limit theorem. digital.library.unt.edu/ark:/67531/metadc174698/
Collective behavior and evolutionary games - An introduction
Article on collective behaviors and evolutionary games. Abstract: This is an introduction to the special issue titled "Collective behavior and evolutionary games" that is in the making at Chaos, Solitons & Fractals. The term collective behavior covers many different phenomena in nature and society. From bird flocks and fish swarms to social movements and herding effects, it is the lack of a central planner that makes the spontaneous emergence of sometimes beautifully ordered and seemingly meticulously designed behavior all the more sensational and intriguing. The goal of the special issue is to attract submissions that identify unifying principles that describe the essential aspects of collective behavior, and which thus allow for a better interpretation and foster the understanding of the complexity arising in such systems. As the title of the special issue suggests, the later may come from the realm of evolutionary games, but this is certainly not a necessity, neither for this special issue, and certainly not in general. Interdisciplinary work on all aspects of collective behavior, regardless of background and motivation, and including synchronization and human cognition, is very welcome. digital.library.unt.edu/ark:/67531/metadc174707/
Complexity and Synchronization
Complexity and the Fractional Calculus
Paper discussing complexity and fractional calculus. Abstract: We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories each of which satisfies the stochastic central limit theorem and the condition for the Mittag-Leffler universality. digital.library.unt.edu/ark:/67531/metadc174709/
Compression and Diffusion: A Joint Approach to Detect Complexity
Article discussing a joint approach to detect complexity by combining the Compression Algorithm Sensitive To Regularity (CASToRe) and Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA) procedures. digital.library.unt.edu/ark:/67531/metadc139462/
Conflict between trajectories and density description: the statistical source of disagreement
Paper discussing the statistical source of disagreement between trajectories and density description. Abstract: We study an idealized version of intermittent process leading the fluctuations of a stochastic dichotomous variable. It consists of an overdamped and symmetric potential well with a cusp-like minimum. The right-hand and left-hand portions of the potential corresponds to = W and = W, respectively. When the particle reaches this minimum is injected back to a different and randomly chosen position, still within the potential well. We build up the corresponding Frobenius-Perron equation and we evaluate the correlation function of the stochastic variable, called (t). We assign the potential well a form yielding (t) = (T = (t=T)), with > 0. Thanks to the symmetry of potential, there are no biases, and we limit ourselves to considering correlation functions with an even number of times, indicated for concision, by h12i, h1234i, and more, in general, by h1:::2ni. The adoption of a formal treatment, based on density, and thus of the operator driving the density time evolution, establishes a prescription for the evaluation of the correlation functions, yielding h1::2ni - h12i:::h(2n 1)2ni. We study the same dynamic problem using trajectories, and we establish that the resulting two-time correlation function coincides with that ordered by the density picture, as it should. We then study the four-times correlation function and we prove that in the non-Poisson case it departs from the density prescription, namely, from h1234i=h12ih34i. We conclude that this is the main reason why the two pictures yield two different diffusion processes, as noticed in an earlier work. [M. Bologna, P. Grigolini, B. J. West, Chem. Phys. 284, (1-2) 115-128 (2002)]. digital.library.unt.edu/ark:/67531/metadc174689/
Cooperation in neural systems: Bridging complexity and periodicity
This article discusses cooperation in neural systems. Abstract: Inverse power law distributions are generally interpreted as a manifestation of complexity, and waiting time distributions with power index μ < 2 reflect the occurrence of ergodicity-breaking renewal events. In this paper we show how to combine these properties with the apparently foreign clocklike nature of biological processes. We use a two-dimensional regular network of leaky integrate-and-fire neurons, each of which is linked to its four nearest neighbors, to show that both complexity and periodicity are generated by locality breakdown: Links of increasing strength have the effect of turning local interactions into long-range interactions, thereby generating time complexity followed by time periodicity. Increasing the density of neuron firings reduces the influence of periodicity, thus creating a cooperation-induced renewal condition that is distinctly non-Poissonian. digital.library.unt.edu/ark:/67531/metadc132986/
Cooperation-induced topological complexity: a promising road to fault tolerance and Hebbian learning
Correlation Function and Generalized Master Equation of Arbitrary Age
This article discusses correlation function and generalized master equation of arbitrary age using non-Poisson, Markovian, and Liouville methods. digital.library.unt.edu/ark:/67531/metadc40401/
Criticality and Transmission of Information in a Swarm of Cooperative Units
This article discusses criticality and transmission of information in a swarm of cooperative units. Abstract: We show that the intelligence of a swarm of cooperative units (birds) emerges at criticality, as an effect of the joint action of frequent organizational collapses and of spatial correlation as extended as the flock size. The organizational collapses make the birds become independent of one another, thereby allowing the flock to follow the direction of the lookout birds. Long-range correlation violates the principle of locality, making the lookout birds transmit information on either danger or resources with a time delay determined by the time distance between two consecutive collapses. digital.library.unt.edu/ark:/67531/metadc40392/
Decoherence, wave function collapses and non-ordinary statistical mechanics
Article discussing decoherence, wave function collapses, and non-ordinary statistical mechanics. Abstract: We consider a toy model of pointer interacting with a 1/2-spin system, whose $\sigma_{x}$ variable is \emph{measured} by the environment, according to the prescription of decoherence theory. If the environment measuring the variable $\sigma_{x}$ yields ordinary statistical mechanics, the pointer sensitive to the 1/2-spin system undergoes the same, exponential, relaxation regardless of whether real collapses or an entanglement with the environment, mimicking the effect of real collapses, occur. In the case of non-ordinary statistical mechanics the occurrence of real collapses make the pointer still relax exponentially in time, while the equivalent picture in terms of reduced density matrix generates an inverse power law relaxation. digital.library.unt.edu/ark:/67531/metadc174684/
Detection of invisible and crucial events: from seismic fluctuations to the war against terrorism
Paper discussing the detection of invisible and crucial events. Abstract: We argue that the recent discovery of the non-Poissonian statistics of the seismic main-shocks is a special case of a more general approach to the detection of the distribution of the time increments between one crucial but invisible event and the next. We make the conjecture that the proposed approach can be applied to the analysis of terrorist network with significant benefits for the Intelligence Community. digital.library.unt.edu/ark:/67531/metadc174695/
Diffusion Entropy and Waiting Time Statistics of Hard-X-Ray Solar Flares
Dynamic Approach to the Thermodynamics of Superdiffusion
This article discusses dynamic approach to the thermodynamics of superdiffusion. Abstract: We address the problem of relating thermodynamics to mechanics in the case of microscopic dynamics without a finite time scale. The solution is obtained by expressing the Tsallis entropic index q as a function of the Lévy index α, and using dynamic rather than probabilistic arguments. digital.library.unt.edu/ark:/67531/metadc77167/
Dynamical approach to Lévy processes
This article discusses a dynamical approach to Lévy processes, which makes it possible to derive all statistical properties of the diffusion process from the correlation function of the dichotomous fluctuating variable Φy(t). digital.library.unt.edu/ark:/67531/metadc139498/
Dynamical model for DNA sequences
This article discusses a dynamical model for DNA sequences based on the assumption that the statistical properties of DNA paths are determined by the joint action of two processes, one deterministic with long-range correlations and the other random and δ-function correlated. digital.library.unt.edu/ark:/67531/metadc139499/
Dynamical Origin of Memory and Renewal
This article discusses a dynamical origin of memory and renewal. Abstract: We show that the dynamic approach to fractional Brownian motion (FBM) establishes a link between a non-Poisson renewal process with abrupt jumps resetting to zero the system's memory and correlated dynamic processes, whose individual trajectories keep a nonvanishing memory of their past time evolution. It is well known that the recrossings of the origin by an ordinary one-dimensional diffusion trajectory generates a Lévy (and thus renewal) process of index θ=1/2. We prove with theoretical and numerical arguments that this is the special case of a more general condition, insofar as the recrossings produced by the dynamic FBM generates a Lévy process with 0<θ<1. This result is extended to produce a satisfactory model for the fluorescent signal of blinking quantum dots. digital.library.unt.edu/ark:/67531/metadc40399/
The Dynamics of EEG Entropy
This article discusses the dynamics of EEG entropy. Abstract: EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context. digital.library.unt.edu/ark:/67531/metadc132967/
Dynamics of Electroencephalogram Entropy and Pitfalls of Scaling Detection
This article discusses dynamics of electroencephalogram entropy and pitfalls of scaling detection. Herein the authors study the time evolution of diffusion entropy to elucidate the scaling of EGG time series. digital.library.unt.edu/ark:/67531/metadc40408/
Event-Driven Power-Law Relaxation in Weak Turbulence
This article discusses event-driven power-law relaxation in weak turbulence. Abstract: We characterize the spectral properties of weak turbulence in a liquid crystal sample driven by an external electric field, as a function of the applied voltage, and we find a 1/f noise spectrum S(f) ∝ 1/fn within the whole range 0< ɳ <2. We theoretically explore the hypothesis that the system complexity is driven by non-Poisson events resetting the system through creation and annihilation of coherent structures, retaining no memory of previous history (crucial events). The authors study the time asymptotic regime by means of the density ψ(τ) of the time distances between two crucial events, yielding ɳ = 3 - μ, where μ is defined through the long-time form ψ(τ) ∝ 1/τµ, with 1 < µ < 3. The system regression to equilibrium after an abrupt voltage change experimentally confirms the theory, proving violations of the ordinary linear response theory for both ɳ > 1 and ɳ < 1. digital.library.unt.edu/ark:/67531/metadc40395/
Experimental Quenching of Harmonic Stimuli: Universality of Linear Response Theory
This article discusses experimental quenching of harmonic stimuli. Abstract: We show that liquid crystals in the weak turbulence electroconvective regime respond to harmonic perturbations with oscillations whose intensity decay with an inverse power law of time. We use the results of this experiment to prove that this effect is the manifestation of a form of linear response theory (LRT) valid in the out-of-equilibrium case, as well as at thermodynamic equilibrium where it reduces to the ordinary LRT. We argue that this theory is a universal property, which is not confined to physical processes such as turbulent or excitable media, and that it holds true in all possible conditions, and for all possible systems, including a complex networks, thereby establishing a bridge between statistical physics and all the fields of research in complexity. digital.library.unt.edu/ark:/67531/metadc40394/
Fast-computational approach to the evaluation of slow-motion EPR spectra in terms of a generalized Langevin equation
Article discussing a fast-computational approach to the evaluation of slow-motion EPR spectra in terms of a generalized Langevin equation. Abstract: A Mori-type generalized Langevin equation is shown to be the only theoretical tool necessary for setting up a fast-computational method of evaluation EPR spectra. The advantages of this algorithm, concerning memory storage and time consumption, are clearly illustrated by explicitly evaluating the line shape of a nitroxide spin probe both in an isotropic liquid solution and in a liquid-crystal mesophase. This method makes theoretical EPR spectra of an orientating potential renders the EPR spectrum much more sensitive to the details of molecular dynamics, thereby making this a potentially powerful tool for monitoring rotational dynamics in liquid mesophases. digital.library.unt.edu/ark:/67531/metadc181661/
A fluctuating environment as a source of periodic modulation
Article discussing a fluctuating environment as a source of periodic modulation. Abstract: We study the intermittent fluorescence of a single molecule, jumping from the "light on" to the "light off" state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic environmental fluctuations make the distribution of the times of sojourn in the "light off" state depart from the exponential form, and that their succession in time mirrors environmental dynamics. As an illustration, we discuss some recent experimental results, where the environmental fluctuations depend on enzymatic activity. digital.library.unt.edu/ark:/67531/metadc132981/
Fluctuation-dissipation process without a time scale
This article discusses fluctuation-dissipation process without a time scale. Abstract: We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied numerically and theoretically, with a good agreement between theory and numerical treatment. As a result of this assumption the equilibrium distribution departs from the ordinary canonical distribution. The distribution tails are truncated, the distribution border is signaled by sharp peaks, and, in the weak dissipation limit, the central distribution body becomes identical to a truncated Lévy distribution. digital.library.unt.edu/ark:/67531/metadc77161/
Fluctuation-Dissipation Theorem for Event-Dominated Processes
This article discusses fluctuation-dissipation theorem for event-dominated processes. Abstract: We study a system whose dynamics are driven by non-Poisson, renewal, and nonergodic events. We show that external perturbations influencing the times at which these events occur violate the standard fluctuation-dissipation prescription due to renewal aging. The fluctuation-dissipation relation of this Letter is shown to be the linear response limit of an exact expression that has been recently proposed to account for the luminescence decay in a Gibbs ensemble of semiconductor nanocrystals, with intermittent fluorescence. digital.library.unt.edu/ark:/67531/metadc40397/
Fluorescence intermittency in blinking quantum dots: renewal or slow modulation?
Article discussing fluorescence intermittency in blinking quantum dots. Abstract: We study time series produced by the blinking quantum dots, by means of an aging experiment, and we examine the results of this experiment in the light of two distinct approaches to complexity, renewal, and slow modulation. We find that the renewal approach fits the result of the aging experiment, while the slow modulation perspective does not. We make also an attempt at establishing the existence of an intermediate condition. digital.library.unt.edu/ark:/67531/metadc174701/
Fractional Brownian motion as a nonstationary process: An alternative paradigm for DNA sequences
This article discusses fractional Brownian motion as a nonstationary process. The model adopted is compatible with the known biological and physical constraints, namely, it is shown to be consistent with the information of current biological literature on folding as well as with the statistical analyses of DNA sequences. digital.library.unt.edu/ark:/67531/metadc75416/
Fractional calculus as a macroscopic manifestation of randomness
Article discussing fractional calculus as a macroscopic manifestation of randomness. Abstract: We generalize the method of Van Hove [Physica (Amsterdam) 21, 517 (1955)] so as to deal with the case of nonordinary statistical mechanics, that being phenomena with no time-scale separation. We show that in the case of ordinary statistical mechanics, even if the adoption of the Van Hove method imposes randomness upon Hamiltonian dynamics, the resulting statistical process is described using normal calculus techniques. On the other hand, in the case where there is no time-scale separation, this generalized version of Van Hove's method not only imposes randomness upon the microscopic dynamics, but it also transmits randomness to the macroscopic level. As a result, the correct description of macroscopic dynamics has to be expressed in terms of the fractional calculus. digital.library.unt.edu/ark:/67531/metadc77121/
From Knowledge, Knowability and the Search for Objective Randomness to a New Vision of Complexity
Paper discussing knowledge, knowability, and the search for objective randomness to a new vision of complexity. Abstract: Herein we consider various concepts of entropy as measure of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do with our understanding of randomness, irreversibility and unpredictability using physical theory, and these in turn undermine our certainty regarding what we can and what we cannot know about complex phenomena in general. The sources of complexity examined herein appear to be channels for the amplification of naturally occurring randomness in the physical world. Our analysis suggests that when the conditions for the renormalization group apply, this spontaneous randomness, which is not a reflection of our limited knowledge, but a genuine property of nature, does not realize the conventional thermodynamic state, and a new condition, intermediate between the dynamic and the thermodynamic state, emerges. We argue that with this vision of complexity, life, which with ordinary statistical mechanics seems to be foreign to physics, becomes a natural consequence of dynamical processes. digital.library.unt.edu/ark:/67531/metadc174694/
From power law intermittence to macroscopic coherent regime
This article offers discussions from power law intermittence to macroscopic coherent regime. The authors address the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots. digital.library.unt.edu/ark:/67531/metadc132992/
From self-organized to extended criticality