Physica A Statistical Mechanics and its Applications

Cell crawling is an important biological phenomenon because it underlies coordinated cell movement in morphogenesis, cancer and wound healing. This phenomenon is based on protrusion at the cell's leading edge, retraction at the rear, contraction and graded adhesion powered by the dynamics of actin and myosin protein networks. A few one-dimensional models successfully explain an anteroposterior organization of the motile cell, but don't sufficiently explore the viscoelastic nature of the actin-myosin gel. We develop and numerically solve a model of a treadmilling strip of viscoelastic actin-myosin gel. The results show that the strip translocates steadily as a traveling pulse, without changing length, and that protein densities, velocities and stresses become stationary. The simulations closely match the observed forces, movements and protein distributions in the living cell.

We provide a complete thermodynamic solution of a 1D hopping model in the presence of a random potential by obtaining the density of states. Since the partition function is related to the density of states by a Laplace transform, the density of states determines completely the thermodynamic behavior of the system. We have also shown that the transfer matrix technique, or the so-called dynamic programming, used to obtain the density of states in the 1D hopping model may be generalized to tackle a long-standing problem in statistical significance assessment for one of the most important proteomic tasks - peptide sequencing using tandem mass spectrometry data.

Recurrent international financial crises inflict significant damage to societies and stress the need for mechanisms or strategies to control risk and tamper market uncertainties. Unfortunately, the complex network of market interactions often confounds rational approaches to optimize financial risks. Here we show that investors can overcome this complexity and globally minimize risk in portfolio models for any given expected return, provided the relative margin requirement remains below a critical, empirically measurable value. In practice, for markets with centrally regulated margin requirements, a rational stabilization strategy would be keeping margins small enough. This result follows from ground states of the random field spin glass Ising model that can be calculated exactly through convex optimization when relative spin coupling is limited by the norm of the network's Laplacian matrix. In that regime, this novel approach is robust to noise in empirical data and may be also broadly relevant to complex networks with frustrated interactions that are studied throughout scientific fields.

Linear measures such as cross-correlation have been used successfully to determine time delays from the given processes. Such an analysis often precedes identifying possible causal relationships between the observed processes. The present study investigates the impact of a positively correlated driver whose correlation function decreases monotonically with lag on the delay estimation in a two-node acyclic network with one and two-delays. It is shown that cross-correlation analysis of the given processes can result in spurious identification of multiple delays between the driver and the dependent processes. Subsequently, delay estimation of increment process as opposed to the original process under certain implicit constraints is explored. Short-range and long-range correlated driver processes along with those of their coarse-grained counterparts are considered.

Cerebral autoregulation (CA) is an important mechanism that involves dilation and constriction in arterioles to maintain relatively s cerebral blood flow in response to changes of systemic blood pressure. Traditional assessments of CA focus on the changes of cerebral blood flow velocity in response to large blood pressure fluctuations induced by interventions. This approach is not feasible for patients with impaired autoregulation or cardiovascular regulation. Here we propose a newly developed technique-the multimodal pressure-flow (MMPF) analysis, which assesses CA by quantifying nonlinear phase interactions between spontaneous oscillations in blood pressure and flow velocity during resting conditions. We show that CA in healthy subjects can be characterized by specific phase shifts between spontaneous blood pressure and flow velocity oscillations, and the phase shifts are significantly reduced in diabetic subjects. Smaller phase shifts between oscillations in the two variables indicate more passive dependence of blood flow velocity on blood pressure, thus suggesting impaired cerebral autoregulation. Moreover, the reduction of the phase shifts in diabetes is observed not only in previously-recognized effective region of CA (<0.1Hz), but also over the higher frequency range from ~0.1 to 0.4Hz. These findings indicate that Type 2 diabetes alters cerebral blood flow regulation over a wide frequency range and that this alteration can be reliably assessed from spontaneous oscillations in blood pressure and blood flow velocity during resting conditions. We also show that the MMPF method has better performance than traditional approaches based on Fourier transform, and is more sui for the quantification of nonlinear phase interactions between nonstationary biological signals such as blood pressure and blood flow.

Precise reference signals are required to evaluate methods for characterizing a fractal time series. Here we use fGp (fractional Gaussian process) to generate exact fractional Gaussian noise (fGn) reference signals for one-dimensional time series. The average autocorrelation of multiple realizations of fGn converges to the theoretically expected autocorrelation. Two methods commonly used to generate fractal time series, an approximate spectral synthesis (SSM) method and the successive random addition (SRA) method, do not give the correct correlation structures and should be abandoned. Time series from fGp were used to test how well several versions of rescaled range analysis (R/S) and dispersional analysis (Disp) estimate the Hurst coefficient (0 < H < 1.0). Disp is unbiased for H < 0.9 and series length N ≥ 1024, but underestimates H when H > 0.9. R/S-detrended overestimates H for time series with H < 0.7 and underestimates H for H > 0.7. Estimates of H(Ĥ) from all versions of Disp usually have lower bias and variance than those from R/S. All versions of dispersional analysis, Disp, now tested on fGp, are better than we previously thought and are recommended for evaluating time series as long-memory processes.

Discrete fractional Gaussian noise (dFGN) has been proposed as a model for interpreting a wide variety of physiological data. The form of actual spectra of dFGN for frequencies near zero varies as f(1-2H), where 0 < H < 1 is the Hurst coefficient; however, this form for the spectra need not be a good approximation at other frequencies. When H approaches zero, dFGN spectra exhibit the 1 - 2H power-law behavior only over a range of low frequencies that is vanishingly small. When dealing with a time series of finite length drawn from a dFGN process with unknown H, practitioners must deal with estimated spectra in lieu of actual spectra. The most basic spectral estimator is the periodogram. The expected value of the periodogram for dFGN with small H also exhibits non-power-law behavior. At the lowest Fourier frequencies associated with a time series of N values sampled from a dFGN process, the expected value of the periodogram for H approaching zero varies as f(0) rather than f(1-2H). For finite N and small H, the expected value of the periodogram can in fact exhibit a local power-law behavior with a spectral exponent of 1 - 2H at only two distinct frequencies.

The exact analytical result for a class of integrals involving (associated) Legendre polynomials of complicated argument is presented. The method employed can in principle be generalized to integrals involving other special functions. This class of integrals also proves useful in the electrostatic problems in which dielectric spheres are involved, which is of importance in modeling the dynamics of biological macromolecules. In fact, with this solution, a more robust foundation is laid for the Generalized Born method in modeling the dynamics of biomolecules.

The objective of this study was to investigate the effects of local heating on complexity of skin blood flow oscillations (BFO) under prolonged surface pressure in rats. Eleven Sprague-Dawley rats were studied: 7 rats underwent surface pressure with local heating (Δt = 10 °C) and 4 rats underwent pressure without heating. A pressure of 700 mmHg was applied to the right trochanter area of rats for 3 h. Skin blood flow was measured using laser Doppler flowmetry. The loading period was divided into nonoverlapping 30 min epochs. For each epoch, multifractal detrended fluctuation analysis (MDFA) was utilized to compute DFA coefficients and complexity of endothelia related metabolic, neurogenic, and myogenic frequencies of BFO. The results showed that under surface pressure, local heating led to a significant decrease in DFA coefficients of myogenic frequency during the initial epoch of loading period, a sustained decrease in complexity of myogenic frequency, and a significantly higher degree of complexity of metabolic frequency during the later phase of loading period. Surrogate tests showed that the reduction in complexity of myogenic frequency was associated with a loss of nonlinearity whereas increased complexity of metabolic frequency was associated with enhanced nonlinearity. Our results indicate that increased metabolic activity and decreased myogenic response due to local heating manifest themselves not only in magnitudes of metabolic and myogenic frequencies but also in their structural complexity. This study demonstrates the feasibility of using complexity analysis of BFO to monitor the ischemic status of weight-bearing skin and risk of pressure ulcers.

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.

The purpose of this opening talk is to describe examples of recent progress in applying statistical mechanics to biological systems. We first briefly review several biological systems, and then focus on the fractal features characterized by the long-range correlations found recently in DNA sequences containing non-coding material. We discuss the evidence supporting the finding that for sequences containing only coding regions, there are no long-range correlations. We also discuss the recent finding that the exponent alpha characterizing the long-range correlations increases with evolution, and we discuss two related models, the insertion model and the insertion-deletion model, that may account for the presence of long-range correlations. Finally, we summarize the analysis of long-term data on human heartbeats (up to 10(4) heart beats) that supports the possibility that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range "anti-correlations" (a tendency to beat faster is balanced by a tendency to beat slower later on). In contrast, for a group of subjects with severe heart disease, long-range correlations vanish. This finding suggests that the classical theory of homeostasis, according to which stable physiological processes seek to maintain "constancy," should be extended to account for this type of dynamical, far from equilibrium, behavior.

When humans walk, the time duration of each stride varies from one stride to the next. These temporal fluctuations exhibit long-range correlations. It has been suggested that these correlations stem from higher nervous system centers in the brain that control gait cycle timing. Existing proposed models of this phenomenon have focused on neurophysiological mechanisms that might give rise to these long-range correlations, and generally ignored potential alternative mechanical explanations. We hypothesized that a simple mechanical system could also generate similar long-range correlations in stride times. We modified a very simple passive dynamic model of bipedal walking to incorporate forward propulsion through an impulsive force applied to the trailing leg at each push-off. Push-off forces were varied from step to step by incorporating both "sensory" and "motor" noise terms that were regulated by a simple proportional feedback controller. We generated 400 simulations of walking, with different combinations of sensory noise, motor noise, and feedback gain. The stride time data from each simulation were analyzed using detrended fluctuation analysis to compute a scaling exponent, a. This exponent quantified how each stride interval was correlated with previous and subsequent stride intervals over different time scales. For different variations of the noise terms and feedback gain, we obtained short-range correlations (alpha < 0.5), uncorrelated time series (alpha = 0.5), long-range correlations (0.5 < alpha < 1.0), or Brownian motion (alpha > 1.0). Our results indicate that a simple biomechanical model of walking can generate long-range correlations and thus perhaps these correlations are not a complex result of higher level neuronal control, as has been previously suggested.

The function of DNA in cells depends on its interactions with protein molecules, which recognize and act on base sequence patterns along the double helix. These notes aim to introduce basic polymer physics of DNA molecules, biophysics of protein-DNA interactions and their study in single-DNA experiments, and some aspects of large-scale chromosome structure. Mechanisms for control of chromosome topology will also be discussed.

Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.

Previous research has examined how various behaviors scale in cities in relation to their population size. Behavior related to innovation and productivity has been found to increase per capita as the size of the city increases, a phenomenon known as superlinear scaling. Criminal behavior has also been found to scaling superlinearly. Here we examine a variety of prosocial behaviors (e.g., voting and organ donation), which also would be presumed to be categorized into a single class of scaling with population. We find that, unlike productivity and innovation, prosocial behaviors do not scale in a unified manner. We argue how this might be due to the nature of interactions that are distinct for different prosocial behaviors.

A variational method for the classical Liouville equation is introduced that facilitates the development of theories for non-equilibrium classical systems. The method is based on the introduction of a complex-valued auxiliary quantity Ψ that is related to the classical position-momentum probability density ρ via ρ = Ψ*Ψ. A functional of Ψ is developed whose extrema imply that ρ satisfies the Liouville equation. Multiscale methods are used to develop trial functions to be optimized by the variational principle. The present variational principle with multiscale trial functions can capture both the microscopic and the coarse-grained descriptions, thereby yielding theories that account for the two way exchange of information across multiple scales in space and time. Equations of the Smoluchowski form for the coarse-grained state probability density are obtained. Constraints on the initial state of the N-particle probability density for which the aforementioned equation is closed and conserves probability are presented. The methodology has applicability to a wide range of systems including macromolecular assemblies, ionic liquids, and nanoparticles.

Three-scaled windowed variance methods (standard, linear regression detrended, and brdge detrended) for estimating the Hurst coefficient (H) are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation function. The scaled windowed variance methods estimate H for fractional Brownian motion (fBm) signals which are cumulative sums of fractional Gaussian noise (fGn) signals. For all three methods both the bias and standard deviation of estimates are less than 0.05 for series having N ≥ 2(9) points. Estimates for short series (N < 2(8)) are unreliable. To have a 0.95 probability of distinguishing between two signals with true H differing by 0.1, more than 2(15) points are needed. All three methods proved more reliable (based on bias and variance of estimates) than Hurst's rescaled range analysis, periodogram analysis, and autocorrelation analysis, and as reliable as dispersional analysis. The latter methods can only be applied to fGn or differences of fBm, while the scaled windowed variance methods must be applied to fBm or cumulative sums of fGn.

A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5 < H <1, characterizes long memory time series by quantifying the rate of decay of the autocorrelation function. S-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 2(10). A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 2(11).

We present several recent studies based on statistical physics concepts that can be used as diagnostic tools for heart failure. We describe the scaling exponent characterizing the long-range correlations in heartbeat time series as well as the multifractal features recently discovered in heartbeat rhythm. It is found that both features, the long-range correlations and the multifractility, are weaker in cases of heart failure.

By taking into account surface transition layers (STL), the dielectric properties of ferroelectric thin films described by the transverse Ising model are discussed in the framework of the mean field approximation. Functions of the intra-layer and inter-layer couplings are introduced to characterize STL, which makes the model more realistic compared to previous treatment of surface layers using uniform surface exchange interactions and a transverse field. The effects of physical parameters on the dielectric properties are quantified. The results obtained indicate that STL has very strong influence on the dielectric properties of ferroelectric thin films. Some of our theoretical results are in accord with the available experimental data.

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.

We find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects, which is stable over a wide range of time scales. However, a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea. Subtle differences in the distributions for the day- and night-phase dynamics for healthy subjects are detected.

We review evidence supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the correlation is remarkably long range--indeed, base pairs thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene, and utilize this fact to build a Coding Sequence Finder Algorithm, which uses statistical ideas to locate the coding regions of an unknown DNA sequence. Finally, we describe briefly some recent work adapting to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function, and reporting that noncoding regions in eukaryotes display a larger redundancy than coding regions. Specifically, we consider the possibility that this result is solely a consequence of nucleotide concentration differences as first noted by Bonhoeffer and his collaborators. We find that cytosine-guanine (CG) concentration does have a strong "background" effect on redundancy. However, we find that for the purine-pyrimidine binary mapping rule, which is not affected by the difference in CG concentration, the Shannon redundancy for the set of analyzed sequences is larger for noncoding regions compared to coding regions.

We review evidence supporting the idea that the DNA sequence in genes containing non-coding regions is correlated, and that the correlation is remarkably long range--indeed, nucleotides thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene. We resolve the problem of the "non-stationarity" feature of the sequence of base pairs by applying a new algorithm called detrended fluctuation analysis (DFA). We address the claim of Voss that there is no difference in the statistical properties of coding and non-coding regions of DNA by systematically applying the DFA algorithm, as well as standard FFT analysis, to every DNA sequence (33301 coding and 29453 non-coding) in the entire GenBank database. Finally, we describe briefly some recent work showing that the non-coding sequences have certain statistical features in common with natural and artificial languages. Specifically, we adapt to DNA the Zipf approach to analyzing linguistic texts. These statistical properties of non-coding sequences support the possibility that non-coding regions of DNA may carry biological information.

We discuss multiple-time scale properties of neurophysiological control mechanisms, using heart rate and gait regulation as model systems. We find that scaling exponents can be used as prognostic indicators. Furthermore, detection of more subtle degradation of scaling properties may provide a novel early warning system in subjects with a variety of pathologies including those at high risk of sudden death.

We examine the action of natural selection in a periodically changing environment where two competing strains are specialists respectively for each environmental state. When the relative fitness of the strains is subject to a very general class of frequency-dependent selection, we show that coexistence rather than extinction is the likely outcome. This coexistence may be a stable periodic equilibrium, stable limit cycles of varying lengths, or be deterministically chaotic. Our model is applicable to the population dynamics commonly found in many types of viruses.

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The usual way to describe the electromagnetic field in a material is to employ the macroscopic Maxwell equations together with constitutive relations and boundary conditions. The most popular form of all these relations is to introduce the permittivity and permeability. Though the problem of permittivity averaging in composites has a long history, there are still unclear aspects. One aspect concerns the local field E_local which acts on a separate inclusion. The most widespread approximation for E_local is the Clausius-Mossotti-Lorenz-Lorentz (CMLL) formula: E_local=〈E〉+4πP/3 where P is the mean polarization of the material. The well-known Lorentz derivation of the CMLL formula leads to many questions. Even popular text books contain omissions and inaccurate speculations. The rigorous description of the problem is dispersed over several original articles. Here we summarise the results, critically reviewing different approaches

Recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and dynamics of complex networks. in this work, we study the synchronizability of a class of continuous-time dynamical networks with scale-free topologies. Furthermore, we propose a synchronization-optimal growth topology model. We also investigate the robustness of the synchronizability of the scale-free dynamical networks with respect to random and specific removal of nodes.

Recent works show that complex network theory may be a powerful tool in time series analysis. We propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series. An original stock time series, the corresponding return series and its amplitude series are considered. The degree distribution of the original series can be well fitted with a power law, while that of the return series can be well fitted with a Gaussian function. The degree distribution of the amplitude series contains two asymmetric Gaussian branches. Reconstruction of networks from time series is a common problem in diverse research. The proposed strategy may be a reasonable solution to this problem.

Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to scale. These extensions are needed in order to explain the regularities of the empirical distributions of some economic variables.

Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension D was derived using the FDF galaxy volume number densities in the spatially homogeneous standard cosmological model with \Omega_{m_0}=0.3, \Omega_{\Lambda_0}=0.7 and H_0=70 km/s/Mpc. The ratio between the differential and integral number densities \gamma and \gamma* obtained from the red and blue FDF galaxies provides a direct method to estimate D, implying that \gamma and \gamma* vary as power-laws with the cosmological distances. The luminosity distance d_L, galaxy area distance d_G and redshift distance d_z were plotted against their respective number densities to calculate D by linear fitting. It was found that the FDF galaxy distribution is characterized by two single fractal dimensions at successive distance ranges. Two straight lines were fitted to the data, whose slopes change at z ~ 1.3 or z ~ 1.9 depending on the chosen cosmological distance. The average fractal dimension calculated using \gamma* changes from D=1.4^{+0.7}_{-0.6} to D=0.5^{+1.2}_{-0.4} for all galaxies, and D decreases as z increases. Small values of D at high z mean that in the past galaxies were distributed much more sparsely and the large-scale galaxy structure was then possibly dominated by voids. Results of Iribarrem et al. (2014, arXiv:1401.6572) indicating similar fractal features with D=0.6 +- 0.1 in the far-infrared sources of the Herschel/PACS evolutionary probe (PEP) at 1.5<z<3.2 are also mentioned.

Multidensity integral equation theory for a model of an associating fluid forming freely jointed fused hard-sphere chain, is presented. Our approach is based on the Wertheim's polymer Percus-Yevick (PPY) theory supplemented by the ideal chain approximation and can be regarded as an extension of the PPY theory for tangent hard-sphere fluids proposed by Chang and Sandler (J. Chem. Phys. 102, 1995, 437). The radial distribution function and the structure factor are calculated for the different model parameters. We compare the resulting predictions for the intermolecular distribution function with the Monte Carlo simulation results for the fused diatomic system. It is found that the accuracy of the prediction of the structure of such system is realiable in a rather wide range of density. It is shown that structure factor exhibits a peculiarity (so-called pre-peak) at small wave numbers, connected with the formation of relatively large molecular aggregates. The dependence of the pre-peak magnitude on the degree of penetrability is investigated and discussed.

The crossover of a pure (undiluted) Ising system (spin per site probability p=1) to a diluted Ising system (spin per site probability p<0.8) is studied by means of Monte Carlo calculations with p ranging between 1 and 0.8 at intervals of 0.025. The evolution of the self-averaging is analyzed by direct determination of the normalized square widths RM and Rχ as a function of p. We find a monotonous and smooth evolution from the pure to the randomly diluted universality class. The p-dependent transition is found to be indepent of size (L). This property is very convenient for extrapolation towards the randomly diluted universality class avoiding complications resulting from finite size effects.

A method to sort out correlations and decorrelations in stratus cloud formation, persistence and breakup is introduced. The detrended fluctuation analysis (DFA) statistical method is applied to microwave radiometer data. The existence of long-range power-law correlations in stratus cloud liquid water content fluctuations is demonstrated over a 2-h period. Moreover using a finite size (time) interval window, a change from Brownian to non-Brownian fluctuation regimes is clearly shown to define the cloud structure changes. Such findings are similar to those found in DNA and financial data sequences when mosaics of persistent and antipersistent patches are present. The occurrence of these statistics in stratus cloud liquid water content suggests the usefulness of similar studies on cloud-resolving model output and for better meteorological predictability.

We study three sand pile automaton models namely, the critical height, critical slope and the critical Laplacian models in two dimensions, in which the stability criterion of the sand columns depend on the zeroth, first and the second derivatives of the sand height function. We carried out simulations on system sizes up to 2048 × 2048 and up to 108 avalanches were generated. The exponents of the critical height model were calculated by taking into account the strong corrections to scaling. In order to determine the exponents of the critical Laplacian model accurately we introduced a height restriction in the toppling criterion that maintains universality but accelerates convergence to the steady state by orders of magnitude. We see clear scaling in the critical height and the critical Laplacian models and find that they belong to different universality classes. However, we do not find any scaling in the critical slope model.

The culling process in Bootstrap Percolation is Abelian since the final stable configuration does not depend on the details of the updating procedure. An efficient algorithm is devised using this idea for the determination of the bootstrap percolation threshold in two dimension which takes $L^2$ time compared to the $L^3 \log L$ in the conventional method. A generalised Bootstrap Percolation allowing many particles at a site is studied where continuous phase transitions are observed for all values of the threshold parameter. Similar results are also obtained for the continuum Bootstrap Percolation model.

In a model of self-organized criticality unstable sites discharge to just one of their neighbours. For constant discharge ratio α and for a certain range of values of the input energy, avalanches are simple branchless Pólya random walks, and their scaling properties can be derived exactly. If α fluctuates widely enough, avalanches become branched, due to multiple discharges, and behave like those of the stochastic sandpile. At the threshold for branched behaviour, peculiar scaling and anomalous diffusive transport are observed.

The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry. These models are based on the combination of ballistic deposition (BD) and random deposition (RD) models or BD and Family deposition (FD) models. Numerically we find, that for pure RD, FD or BD models the mean height of the percolation deposit $\bar h$ grows with the substrate length $L$ according to the generalized logarithmic law $\bar h\propto (\ln (L))^\gamma$, where $\gamma=1.0$ (RD), $\gamma=0.88\pm 0.020$ (FD) and $\gamma=1.52\pm 0.020$ (BD). For BD model, the scaling law between deposit density $p$ and its mean height $\bar h$ at the point of percolation of type $p-p_\infty \propto \bar h^{-1/\nu_h}$ are observed, where $\nu_h =1.74\pm0.02$ is a scaling coefficient. For competitive models the crossover, %in $h$ versus $L$ corresponding to the RD or FD -like behaviour at small $L$ and the BD-like behaviour at large $L$ are observed. Comment: 8 pages,4 figures, Latex, uses iopart.cls

We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated L\'evy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well describes the scaling and its breakdown observed in empirical data, while it is not able to properly describe the fluctuations of volatility empirically detected. The ARCH(1) and GARCH(1,1) models are able to describe the probability density function of price changes at a given time horizon, but both fail to describe the scaling properties of the PDFs for short time horizons.

This paper presents classical molecular dynamics (MD) simulations of an aluminum slab under a premelting condition. The aluminum surface is set at the (110) orientation. We have used a simple analytical form of an embedded-atom-method (EAM) potential to describe the inter-atomic interactions of the aluminum atoms. The results from our study are compared with those reported by Schommers. The pair correlation function is examined at different temperatures in order to analyze the trends for possible resemblance with Schommers results. The difference in the trends has confirmed that the use of the EAM potential resulted in the occurrence of the premelting condition at a lower temperature than the reported results obtained using the pseudopotential model. The surface melting process is also compared with other works for a better understanding of the effect of the EAM model on premelting of the Al(110) surface.

In vitro, pure DNA forms multiple liquid crystalline phases when the polymer concentration is increased: precholesteric organization, cholesteric phase and columnar hexagonal phase. Similar organizations of chromatin can be found in vivo: hexagonal packing in bacteriophages and certain sperm heads, cholesteric organization in dinoflagellate chromosomes, bacterial nucleoids and mitochondrial DNA, helical-shaped chromosomes in many species. The different forms of condensed chromatin seem to be related to different local concentrations of DNA. In the highly condensed forms, chromatin is inactive and the double stranded DNA molecule is linear with small amounts of associated proteins.A more detailed analysis is presented in the case of cholesteric structures (helical pitch, defects) in polarizing microscopy and in electron microscopy. Differences observed in vitro and in vivo are probably related to the length of the DNA molecule and to the presence of proteins associated to DNA in the chromosomes.

In this paper, the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi-infinite symbolic sequence space Σ2. It is shown that there exists one Bernoulli-measure global attractor of rule 119, which is also the nonwandering set of the rule. Moreover, it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy. Therefore, rule 119 is chaotic in the sense of both Li-Yorke and Devaney on the global attractor. It is interesting that rule 119, a member of Wolfram’s class II which was said to be simple as periodic before, actually possesses a chaotic global attractor in Σ2. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules therein.

For both Northern and Southern hemispheres, the long-term memory dynamics for continent and ocean temperature records in the recent 125 years is studied in this paper. It is found that the records exhibit long-range memory and multifractality characteristics where large temperature anomalies display a more random behavior than the overall time series. A 256-month moving window was used to compute the time evolution of the fractal scaling exponent, giving the following results: (i) Ocean temperatures are more persistent than land temperatures, a result already reported in recent publications, (ii) All records show multifractality features, reflecting the nonlinear behavior of the temperature dynamics. Continent temperatures present sharper multifractal spectra than ocean temperatures, (iii) The persistency, as revealed by the scaling exponent, for ocean temperatures displays a cyclic behavior around a nearly constant average value of 22 years, (iv) The persistency for the Northern Hemisphere land temperature is also cyclical but with an increasing trend, and (v) The time at which the Northern Hemisphere continent temperature persistency will converge into the Northern Hemisphere ocean behavior was estimated with linear and exponential extrapolation functions, showing hitting dates around 2050±20 A.D. Potential implications of these results concerning the nature of climate change are also discussed.

We analyze high-resolution foreign exchange data consisting of 20 million data points of USD-JPY for 13 years to report firm statistical laws in distributions and correlations of exchange rate fluctuations. A conditional probability density analysis clearly shows the existence of trend-following movements at time scale of 8-ticks, about .

In the previous paper we have shown that the classification problem of the homogeneous real 16-vertex models on a square lattice as proposed by Gaaff and Hijmans is closely connected with the similar problem corresponding to the boson Bogoliubov transformation in quantum mechanics. This insight leads us in the present paper to use arguments and examples from papers dealing with the latter problem in a further study of the classification problem of the real 16-vertex models. We also use a somewhat modified concept of “standard (or normal) 16-vertex model” which was introduced by Hijmans and Schram in a similar study concerning the complex 16-vertex models. We show that, rather than the single family found by Hijmans and Schram for the complex variant of the problem, the set of equivalence classes of real 16-vertex models can be divided up into seven families. This strongly suggests the existence of a new type of phase transitions which manifest themselves when the physical system in the 16-parameter space “moves” from one family to another.

We consider the classification of all homogeneous 16-vertex models on a square lattice which was proposed by Gaaff and Hijmans. We show that this classification can be translated into (that is, reformulated in terms of) a classification of matrices which closely resembles one already investigated with some success in the literature, viz. the classification connected with the boson Bogoliubov transformation in quantum mechanics. The main difference between our approach and the one of Gaaff and Hijmans who also made a reformulation, is that we can keep our considerations, in conformity with the actual physical problem, within the field of real rather than complex numbers. In the accompanying paper this leads to results with features not present in the analysis over , which point to a possible connection with a new kind of phase transitions.

In this article, we study the behavior of the stock prices of a subset of eight U.S. industries from the late 1800's to the Great Depression. In particular, we focus on the potential presence of volatility shifts, the persistence of volatility, and on the degree of co-movement of stock returns prior to and during the Great Depression. Our findings show that stock markets became particularly volatile toward the mid 1930's, but that the persistence of volatility tended to decrease around the same time period. In that regard, we find little evidence that such behavior is driven by trading volume. In addition, we conclude that the overall correlation across the different industries was relatively more significant in statistical terms from 1921 to part of the Great Depression (1929–1931; 1933–1934 and 1936).

It is widely believed that the chemical master equation has no rigorous microphysical basis, and hence no a priori claim to validity. This view is challenged here through arguments purporting to show that the chemical master equation is exact for any gas-phase chemical system that is kept well stirred and thermally equilibrated.

Simple crossover equations for the susceptibility and the specific heat in zero field have been obtained on the basis of the renormalization-group method and ε-expansion. The equations contain the Ginzburg number as a parameter. At temperatures near the critical temperature, scaling behavior including the first Wegner corrections is reproduced. At temperatures far away from the critical temperature the classical Landau expansion with square-root corrections is recovered. For small values of the Ginzburg number the crossover equations approach a universal form. The equations are applied to represent experimental specific heat data for CH4, C2H6, Ar, O2 and CO2 along the critical isochore in a universal form.