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Background: There has been an increasing interest in the development and prevention of sports injuries from a complex dynamic systems perspective. From this perspective, injuries may occur following critical fluctuations in the psychophysiological state of an athlete. Our objective was to quantify these so-called Early Warning Signals (EWS) as a proof of concept to determine their explanatory performance for injuries. The sample consisted of 23 professional youth football (soccer) players. Self-reports of psychological and physiological factors as well as data from heart rate and GPS sensors were gathered on every training and match day over two competitive seasons, which resulted in an average of 339 observations per player (range = 155–430). We calculated the Dynamic Complexity (DC) index of these data, representing a metric of critical fluctuations. Next, we used this EWS to predict injuries (traumatic and overuse). Results: Results showed a significant peak of DC in 30% of the incurred injuries, in the six data points (roughly one and a half weeks) before the injury. The warning signal exhibited a specificity of 95%, that is, correctly classifying non-injury instances. We followed up on this promising result with additional calculations to account for the naturally imbalanced data (fewer injuries than non-injuries). The relatively low F1 we obtained (0.08) suggests that the model's overall ability to discriminate between injuries and non-injuries is rather poor, due to the high false positive rate. Conclusion: By detecting critical fluctuations preceding one-third of the injuries, this study provided support for the complex systems theory of injuries. Furthermore, it suggests that increasing critical fluctuations may be seen as an EWS on which practitioners can intervene. Yet, the relatively high false positive rate on the entire data set, including periods without injuries, suggests critical fluctuations may also precede transitions to other (e.g., stronger) states. Future research should therefore dig deeper into the meaning of critical fluctuations in the psychophysiological states of athletes. Key Points: Complex Systems Theory suggests that sports injuries may be preceded by a warning signal characterized by a short window of increased critical fluctuations. Results of the current study showed such increased critical fluctuations before 30% of the injuries. Across the entire data set, we also found a considerable number of critical fluctuations that were not followed by an injury, suggesting that the warning signal may also precede transitions to other (e.g., healthier) states. Increased critical fluctuations may be interpreted as a window of opportunity for the practitioner to launch timely and targeted interventions, and researchers should dig deeper into the meaning of such fluctuations. [ABSTRACT FROM AUTHOR]

Objective: Depressive symptom dynamics, including change trajectories and symptom variability, have been related to therapy outcomes. However, such dynamics have often been examined separately and related to outcomes of interest using two-step analyses, which are characterized by several limitations. Here, we show how to overcome these limitations using location-scale models in a dynamic structural equation modeling framework. Method: We introduce location-scale modeling in an accessible manner to pave the way for its use in research integrating within-person dynamics and intervention-related change in psychopathology, and we illustrate this modeling approach in a large-scale internet-based intervention for depression (N = 1,656). Using eight data points sampled across about 8 weeks, we predicted improvement across the intervention (50% symptom reduction) as a function of early change and symptom variability. Results: Early symptom change was associated with a more likely improvement across therapy. Variability of symptoms beyond change trajectories during the intervention was associated with less likely improvement. Conclusions: Location-scale models, and dynamic structural equation modeling more generally, are well suited to modeling how patterns of symptom change during psychotherapy are related to important (e.g., therapy) outcomes. Our illustrative application of location-scale modeling showed that symptom variability was associated with less overall improvement in depressive symptoms. However, this finding requires replication with more intensive sampling of symptoms before final conclusions can be drawn on when and how to distinguish maladaptive from adaptive variability during psychotherapy. What is the public health significance of this article?: During psychotherapy, multiple mechanisms of change should work simultaneously and in concert. As this study highlights, it is important to examine multiple types of symptom dynamics during psychotherapy simultaneously to understand the processes and ultimately the causes of therapeutic change. [ABSTRACT FROM AUTHOR]

While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ , ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM. [ABSTRACT FROM AUTHOR]

We show hereby that recycling of NdFeB permanent magnets by selective leaching and precipitation is possible, using an electrolyte as hydrotrope, thus avoiding the need of any specific extractant molecules. We analyse the yield of the extractant-free process and show that the non toxic formulation of Sodium Salicylate and ethylacetate used as diluent and choosing the optimal tie-line in a ternary phase diagram allows extraction using any type of acid in the aqueous phase. Iron is well separated from rare earths and the product can be recovered directly form the fluid used in separation by oxalic acid precipitation.

In this work, we compared the shape of a binodal curve in the ternary systems "water – methanol – chloroform", "water – methanol – dichloromethane", "water – tert-butanol – toluene", and "water – 2-butoxyethanol – toluene" in the vicinity of the liquid-liquid critical point (LLCP). We have shown that different approaches to characterize the binodal shape are not equivalent for real ternary systems. The preferred approach involves the calculation of distances based on the tangent to the LLCP and the perpendicular lines to the points on the binodal. The variability in the apparent degree of the binodal curve is revealed, contrary to the known literature. [ABSTRACT FROM AUTHOR]

While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ, ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM.

We study the critical fluctuations near the resistive transition of very thin films of high-temperature cuprate superconductors composed of a number N of only a few unit cells of superconducting bilayers. For that, we solve the fluctuation spectrum of a Gaussian–Ginzburg–Landau model for few-bilayers superconductors considering two alternating Josephson interlayer interaction strengths, and we obtain the corresponding paraconductivity above the transition. Then, we extend these calculations to temperatures below the transition through expressions for the Ginzburg number and Kosterlitz–Thouless-like critical region. When compared with previously available data in YBa 2 Cu 3 O 7 − δ few-bilayers systems, with N = 1 to 4, our results seem to provide a plausible scenario for their critical regime. [ABSTRACT FROM AUTHOR]

The quantum origin of the cuprate pseudogap and its relationship to symmetry-breaking orders is a central conundrum of unconventional superconductors. The difficulty is deeply rooted in modeling simultaneous organizations in multiple degrees of freedom (including spin, momentum, and real space) generated by strong electron-electron correlations. Beyond early theories focusing on the description in spin and momentum space, recent studies turn to examine the spatial organization and intertwining mechanism of multiple orders. In this review, we summarize some progress in understanding the spatial organization of critical fluctuations and highlight the recent discovery of a universal energy-length scaling. This scaling quantitatively explains the nontrivial magnitude and doping dependence of the pseudogap energy and critical temperature and their relations to charge and superconducting ordering. We close with a prospect of the spatial organization mechanism of intertwined orders and its possible composite energy scaling.

In this work, we studied the water-2-butoxyethanol-toluene, water-methanol-chloroform, and water-methanol-dichloromethane ternary systems. The position of the separation boundary was experimentally determined and approximated by various functions. We elucidated the major factors hindering satisfactory approximation of separation boundaries by empirical functions with a small number of adjustable parameters. The approximation of separation boundaries in ternary systems can be carried out using polynomial and smoothing spline functions with error comparable to experimental uncertainty. [ABSTRACT FROM AUTHOR]

We study the critical fluctuations near the resistive transition of very thin films of high-temperature cuprate superconductors composed of a number N of only a few unit cells of superconducting bilayers. For that, we solve the fluctuation spectrum of a Gaussian–Ginzburg–Landau model for few-bilayers superconductors considering two alternating Josephson interlayer interaction strengths, and we obtain the corresponding paraconductivity above the transition. Then, we extend these calculations to temperatures below the transition through expressions for the Ginzburg number and Kosterlitz–Thouless-like critical region. When compared with previously available data in YBa2Cu3O7−δ few-bilayers systems, with N = 1 to 4, our results seem to provide a plausible scenario for their critical regime.

Liquid-liquid phase-separating lipid membranes belong to the 2-D Ising universality class. While their in-plane critical behaviors are well studied, how the behaviors modulate out-of-plane interactions is rarely explored, despite its profound implications for biomembranes and 2-D ferromagnets. Here, we examine how the interlayer interaction, manifested as membrane fusion, is affected by the membranes’ critical fluctuations. Remarkably, the critical fluctuations suppress membrane fusion, suggesting a correlation between critical behaviors and interlayer interactions for 2-D Ising systems.

Abstract: The conventional view on interventions as mechanistically causing interchangeable clients to get better has come under attack. Group-based and linear approaches fall short in adequately describing the idiosyncratic and dynamic nature of treatment processes. Non-linear dynamic system theories in contrast hold great potential to better conceptualize and understand the generalities and idiosyncrasies of psychotherapeutic change processes. The aim of this study was to examine whether we can detect markers of complex dynamical systems behavior in two single-case therapies. All sessions from both therapies were coded with sequential plan analysis using a 10s sampling frequency. The coding system incorporates verbal and non-verbal behaviors and allows for the representation of contextualized interactive behaviors. The high sampling frequency results in long time series, which allowed us to apply non-linear analysis techniques. We found strong support for complex behavior and the existence of a butterfly effect, i.e., a relatively short prediction horizon in which reliable predictions about the system’s future behavior could be made. Further, critical fluctuations as a marker for phase-transitions were detected that were accompanied with different interactional patterns in both therapies. Finally, there was strong support for self-organized pattern formation, with a few interactional patterns dominating the interaction. Considering that we are intervening on complex dynamical systems means that we have to (1) acknowledge the principal individuality of change processes, (2) accept the fundamental limitations of the mechanistic input-output model of treatment effects and (3) appreciate the impossibility of long-term predictions of treatment responses.

Critical fluctuations are known to induce a collapse of polymer chains in a mixed solvent upon approaching its liquid–liquid critical point, as originally predicted by Brochard and de Gennes. Recently, we have found that closer to the critical point this collapse is followed by a reswelling of the polymer coils well beyond the original dimensions, a phenomenon not predicted by the theory of Brochard and de Gennes. We submit that upon approaching the critical temperature more closely, the correlation length of the critical fluctuations inside the polymer coils can no longer further increase due to the finite size of the coils, resulting in the appearance of large critical Casimir forces that cause a significant expansion of the polymer coils. Eventually, micro-phase separation inside the coils will appear and the coils will reshrink. This entire process takes place while the bulk solution is still in the one-phase region. [ABSTRACT FROM AUTHOR]

This paper explains how a first principles theory for critical fluctuations consisting of isothermal fourth sound waves in bulk liquid He II can be tested experimentally. The first principles theory is able to predict the detailed behavior of isothermal fourth sound wave signals very near the lambda transition. Experimental detection of the predicted signals would validate this theory to a high degree of confidence and thereby provide a new paradigm for understanding the physical mechanism responsible for critical properties in liquid helium 4. Theoretical and experimental results that support the predictions of this theory are presented. The method of detection rests on formulas derived here for the time-dependent density-density correlation function and associated pressure fluctuations in superfluid He II that is in thermodynamic equilibrium near the lambda transition temperature. Plots of predicted signals are presented and experimental apparatus that uses an electron-tunneling sensor that can detect the pressure fluctuations is described. Some implications of how validation of this first principles theory would impact general understanding of critical fluctuations and lambda transitions are discussed. • The goal is to validate the microscopic-based isothermal fourth sound theory. • Successful validation would solve important long-standing problems for liquid 4He. • Provide a paradigm that could be applied in explaining critical properties. • This approach is an alternative to Renormalization Group theory. [ABSTRACT FROM AUTHOR]

Abstract An investigation into the superconducting order parameter thermodynamic fluctuations and their manifestations on paraconductivity in cuprate superconductors is done using a renormalized Gaussian approach based on the Ginzburg–Landau theory. The temperature dependence of paraconductivity is affected by repulsive interactions between Cooper pairs and does not follow the universal power laws predicted by the conventional Aslamazov–Larkin theory. In addition to the well known Lawrence–Doniach crossover from three to two dimensions, we also highlight the crossover from one-dimensional to two-dimensional behavior and the crossover from weak two-dimensional to strong two-dimensional critical behavior in the vicinity of the critical temperature. These dimensional crossovers result from the resistance between Cooper pairs due to critical and thermal fluctuations which cause a transition from a metastable state to one with a smaller current. Two illustrative examples (the cases of YBa 2 Cu 3 O 6.9 and Bi 2 Sr 2 Ca Cu 3 0 x compounds) are provided in support of the analysis, so as to demonstrate the usefulness of the approach. Highlights • A depairing factor is incorporated in the Ginzburg–Landau model for paraconductivity. • Method reveals a crossover from one-dimensional to two-dimensional critical behavior. • Crossover from weak to strong two-dimensional critical behavior is also highlighted. • The discussion considers phase fluctuations due to inhomogeneities in given materials. • Expressions obtained are valid over a wide range of temperatures and dimensions. [ABSTRACT FROM AUTHOR]

Highlights • Improved GL theory for fluctuations in localized ferromagnets and amorphous magnets. • Model accounts for the geometry and strongly correlated nature of systems. • New phenomenology accounts for dimensionality and localized character of systems. • Approach is capable of describing both the critical and near-critical regimes. • Model provides a unified picture for the Gaussian and critical regimes. Abstract This paper gives a model field-theoretic description of thermodynamic magnetization fluctuations and exchange interactions in localized ferromagnets and amorphous magnets. A local Ginzburg-Landau type Hamiltonian is used to describe the properties observed in the transition region. The approach provides another method of tackling interacting spin systems dominated by size effects, fluctuations and correlations, which lead to a dimensional phenomenology of critical behavior. It is also found that the competition between long- and short-range interactions gives rise to the redistribution of the density of spins and causes the anisotropy of the electron spectrum. Above the upper-critical dimension, the approach behaves like mean-field theory with however, thermodynamic quantities modified by intrinsic critical fluctuations, whereas it predicts correctly the universal quantities for dimension 4 and below. At all temperatures, the model matches the magnetic observables, thus providing a unified picture for both the Gaussian and critical regimes. [ABSTRACT FROM AUTHOR]

The method of Heun's differential equation is demonstrated in studying a fractional linear birth–death process (FLBDP) with long memory described by a master equation. The exact analytic solution of the generating function for the probability density is obtained on the basis of Heun's differential equation. The multi-fractal nature of FLBDP associated with long memory is demonstrated in conjunction with the present simple birth–death process. Finally, the subtle multi-fractal nature of critical fluctuations under long memory is also displayed in the present FLBDP. Further, discussions are also given on the features of transient fluctuation in systems with long memory. [ABSTRACT FROM AUTHOR]

The description of dynamical fluctuations near the QCD critical point in heavy-ion collisions is crucial for understanding the existing and upcoming experimental data from the beam energy scan programs. In this talk we discuss the evolution of fluctuations of the net-baryon density as given by a stochastic diffusion equation. We study equilibrium as well as dynamical systems for which we can show the impact of nonequilibrium effects on the second-order moment. [ABSTRACT FROM AUTHOR]

We study fluctuations of the sigma field and the net-baryon number on the crossover side of the critical point within the model of nonequilibrium chiral fluid dynamics (N χ FD). Herein, the sigma field as the chiral order parameter is propagated explicitly and coupled to a fluid of quarks. Before investigating these fluctuations in an expanding nonequilibrium medium, we scrutinize the N χ FD model by comparing cumulants of the sigma fluctuations in a thermalized box to (ratios of) susceptibilities as they are obtained from derivatives of the grand canonical potential. The dynamically determined cumulants follow the trend of the thermodynamic susceptibilities. In an expanding inhomogeneous medium, however, the behavior of the fluctuations is shown to be different as a result of memory effects. [ABSTRACT FROM AUTHOR]

We generalize and apply the key elements of the Kibble-Zurek framework of nonequilibrium phase transitions to study the non-equilibrium critical cumulants near the QCD critical point. We demonstrate that the off-equilibrium critical cumulants are expressible as universal scaling functions. We discuss how to use off-equilibrium scaling to provide powerful model-independent guidance in searches for the QCD critical point. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Markov process whose unique invariant distribution is the Curie-Weiss model of self-organized criticality (SOC) we designed and studied in (Ann. Probab. 44(1):444-478, 2016). In the Gaussian case, we prove rigorously that it is a dynamical model of SOC: the fluctuations of the sum Sn (⋅) of the process evolve in a time scale of order √n and in a space scale of order n3/4 and the limiting process is the solution of a "critical" stochastic differential equation. [ABSTRACT FROM AUTHOR]

The fluid mosaic model proposed by Singer and Nicolson established a powerful framework to interrogate biological membranes that has stood the test of time. They proposed that the membrane is a simple fluid, meaning that proteins and lipids are randomly distributed over distances larger than those dictated by direct interactions. Here we present an update to this model that describes a spatially adaptable fluid membrane capable of tuning local composition in response to forces originating outside the membrane plane. This revision is rooted in the thermodynamics of lipid mixtures, draws from recent experimental results, and suggests new modes of membrane function. • Spatially adaptable membranes are fluids with high compositional susceptibility. • Thermal forces produce spontaneous, dynamic domains within adaptable membranes. • Extended, long-lived domains can be induced by forces beyond the membrane plane. • Hallmarks of an adaptable membrane are observed in model and cell plasma membranes. • A adaptable fluid mosaic suggests new modes of plasma membrane function. [ABSTRACT FROM AUTHOR]

We report on recent progress in the study of the evolution of non-Gaussian cumulants of critical fluctuations. We explore the implications of non-equilibrium effects on the search for the QCD critical point. [ABSTRACT FROM AUTHOR]

Immune receptors that specifically recognize foreign antigens to activate leukocytes in adaptive immune responses belong to a family of multichain cell surface proteins. All of these contain immunoreceptor tyrosine-based activation motifs in one or more subunits that initiate signaling cascades following stimulated tyrosine phosphorylation by Src-family kinases. As highlighted in this review, lipids participate in this initial activation step, as well as in more downstream signaling steps. We summarize evidence for cholesterol-dependent ordered lipids serving to regulate the store-operated Ca 2 + channel, Orai1, and we describe the sensitivity of Orai1 coupling to the ER Ca 2 + sensor, STIM1, to inhibition by polyunsaturated fatty acids. Phosphoinositides play key roles in regulating STIM1-Orai1 coupling, as well as in the stimulated Ca 2 + oscillations that are a consequence of IgE receptor signaling in mast cells. They also participate in the coupling between the plasma membrane and the actin cytoskeleton, which regulates immune receptor responses in T cells, B cells, and mast cells, both positively and negatively, depending on the cellular context. Recent studies show that other phospholipids with mostly saturated acylation also participate in coupling between receptors and the actin cytoskeleton. Lipid heterogeneity is a central feature of the intimate relationship between the plasma membrane and the actin cytoskeleton. The detailed nature of these interactions and how they are dynamically regulated to initiate and propagate receptor-mediated cell signaling are challenging questions for further investigation. This article is part of a Special Issue entitled: The cellular lipid landscape edited by Tim P. Levine and Anant K. Menon. [ABSTRACT FROM AUTHOR]

Visually detecting nanoscopic structures in lipid membranes is important for elucidating lipid–lipid interactions, which are suggested to play a role in mediating membrane rafts. We use solution atomic force microscopy (AFM) to study lateral and normal organization in multicomponent lipid membranes supported by mica substrate. Nanoscopic heterogeneity is observed in a three-component system composed of 1-palmitoyl-2-oleoyl- sn -glycero-3-phosphocholine (POPC)/brain-sphingomyelin (bSM)/cholesterol (Chol). We find sub-ten-nanometer correlation lengths that are used to describe membrane lateral organization. In addition, we find that the correlation length is independent on cholesterol concentration, while the height fluctuation (variation) is not. To explore the mechanism that controls the size of membrane heterogeneity, we extend our study to a four-component system composed of 1,2-dioleoyl- sn -glycero-3-phosphocholine (DOPC)/POPC/bSM/Chol. By systematically adjusting the relative amount of DOPC and POPC, we obtain macroscopic-to-nanoscopic size transition of membrane heterogeneity. In contrast to the results from vesicle based fluorescence microscopy, we find that the structural transition is continuous both in the lateral and normal directions. We compare our nanoscopic structures to two theoretical models, and find that both the critical fluctuations and the nanodomain models are not sufficient to account for our solution AFM data. Finally, we propose a nanoheterogeneity model that could serve as the organization principle of the observed nanoscopic structures in multicomponent lipid membranes. [ABSTRACT FROM AUTHOR]

A first principles theory of the λ transition in liquid 4 He was introduced in a recent paper [H. W. Jackson, J. Low Temp. Phys. 155, 1 (2009)]. In that theory critical fluctuations consisting of isothermal fourth sound waves are treated with quantum statistical mechanics methods in deriving formulas for constant volume conditions for specific heat, correlation length, equal time pair correlation function, and isothermal compressibility. To leading order terms in ( T λ − T ) the theory yields exact results α ′=0 and ν ′=2/3 for critical exponents at constant volume. A follow-up study in the present paper demonstrates by a least squares fit that a logarithmic function accurately describes the specific heat at svp when ( T λ − T ) is between 10 −9 K and 10 −5 K. This logarithmic divergent behavior conflicts with previous analyses of experimental data and predictions of renormalization group theory that constant pressure specific heat is finite at T λ , but Is thermodynamically consistent with logarithmic asymptotic behavior of specific heat at constant volume predicted in the new theory. The first principles theory is extended in this paper to derive formulas for superfluid density and for a relation between superfluid density and correlation length in He II near T λ . Numerical results based on these formulas are in good agreement with experimental data produced by second sound measurements. [ABSTRACT FROM AUTHOR]

Liquid-liquid phase-separating lipid membranes belong to the 2-D Ising universality class. While their in-plane critical behaviors are well studied, how the behaviors modulate out-of-plane interactions is rarely explored, despite its profound implications for biomembranes and 2-D ferromagnets. Here, we examine how the interlayer interaction, manifested as membrane fusion, is affected by the membranes' critical fluctuations. Remarkably, the critical fluctuations suppress membrane fusion, suggesting a correlation between critical behaviors and interlayer interactions for 2-D Ising systems.

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human EEG, however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where nonlinearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power-law scaling and bistable switching have been suggested as generic indicators of the approach to bifurcation in nonlinear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen-Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations.

The paper points out the impact of modern theory methods of synergetic over the analysis of sociology and economics. These methods are able to capture much more subtle and complicated issues on which the society rules are based. The society is a nonlinear system with a hierarchy of instabilities, entailing the occurrence of increasingly complex collective structures. The factors responsible for this innovative change are the fluctuations, the subjective elements or the unusual decisions which are basically neglected in the classic type models. Nevertheless, at the moment when the parameters of mechanisms related to the evolution and interaction between individuals reach a critical level, these nonessential innovative factors are encouraged and are able to overthrow the global order. [ABSTRACT FROM AUTHOR]

Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human electroencephalography (EEG), however, have shown significant autocor relation at time lags on the scale of minutes, indicating the need to consider regimes where non-linearities influence the dynamics. Statistical properties such as increased autocorre lation length, increased variance, power law scaling, and bistable switching have been suggested as generic indicators of the approach to bifurcation in non-linear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen-Rit model) of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations. [ABSTRACT FROM AUTHOR]

We report on the quantitative parameters of fluctuation effects observed in the birefringence and linear thermal expansion of Sn2P2(SexS1-x)6 crystals with x = 0 and 0.28. These parameters, including the Ginzburg number that governs the temperature width of the scaling region, are found to be of the same order of magnitude. The relevant implications concerned with the influence of structural defects and multicritical points on the phase diagram are discussed [ABSTRACT FROM AUTHOR]

Abstract: The critical scattering in the cubic noncentrosymmetrical helimagnets with Dzyaloshinskii–Moriya interaction (, 0.2, and 0.5) has been studied. The samples with small Co concentration () are found to give the critical scattering with the q-dependence of the typical Lorentzian shape. The critical index of the inverse correlation length is found for the compound with . The critical scattering above has not been observed for . The critical index of the order parameter for the compounds with and are equal to and , respectively. The value of could not been established for because of the first order character of the phase transition. In our opinion, the change of the character of the phase transition from the weakly first order to the real first order type with increase of the Co concentration is related to the decrease of the anisotropy and increase of the itinerancy of the compounds under study. [Copyright &y& Elsevier]

Abstract: We studied multisegmental coordination and stride characteristics in nine participants while walking and running on a treadmill. The study’s main aim was to evaluate the coordination patterns of walking and running and their variance as a function of locomotion speed, with a specific focus on gait transitions and accompanying features like hysteresis and critical fluctuations. Stride characteristics changed systematically with speed in a gait-dependent fashion, but exhibited no hysteresis. Multisegmental coordination of walking and running was captured by four principal components, the first two of which were present in both gaits. Locomotion speed had subtle yet systematic differential effects on the relative phasing between the identified components in both walking and running and its variance, in particular in the immediate vicinity of gait transitions. Unlike the stride characteristics, the identified coordination patterns revealed clear evidence of both hysteresis and critical fluctuations around transition points. Overall, the results suggest that walking and running entail similar, albeit speed- and gait-dependent, coordination structures, and that gait transitions bear signatures of nonequilibrium phase transitions. Application of multivariate analyses of whole-body recordings appears crucial to detect these features in a reliable fashion. [Copyright &y& Elsevier]

We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field. We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼ r 4− d . [ABSTRACT FROM AUTHOR]

It is pointed out that the dynamics of the order parameter at a thermal critical point obeys the precepts of the nonextensive Tsallis statistics. We arrive at this conclusion by putting together two well-defined statistical–mechanical developments. The first is that critical fluctuations are correctly described by the dynamics of an intermittent nonlinear map. The second is that intermittency in the neighborhood of a tangent bifurcation in such map rigorously obeys nonextensive statistics. We comment on the implications of this result. [Copyright &y& Elsevier]

Carbon doping of magnesium diboride resulting in the Mg(B0.9C0.1)2 stoichiometry leads to the superconducting transition temperature Tc=22 K which is about 17 K less than in the pure MgB2. We present the magnetotransport measurements on the doped polycrystalline samples up to 23 T in the temperature range from 1.5 K. Despite the significantly lowered Tc the upper critical magnetic field Hc2 is much higher here than in the pure MgB2 and achieves values of about 25–30 Tesla at low temperatures comparable to the MgB2 samples with the highest level of impurity scattering. The anomalous temperature dependence Hc2(T) revealing a positive curvature in the overall temperature range is discussed in the framework of the two-gap superconductivity, which is still present here. As another possibility an importance of the critical fluctuations is considered within the Ullah–Dorsey scaling model. [Copyright &y& Elsevier]

It is well known that classical equations of state, like the Van der Waals equation, fail in the region near the critical point of a fluid, where the behavior of the thermodynamic properties is strongly affected by density fluctuations. In this paper, we present a theoretical approach to correct classical cubic equations of state for the effects of critical fluctuations. The approach utilizes a transformation deduced from the renormalization-group theory of critical phenomena that was developed earlier for a classical Landau expansion of the Helmholtz-free-energy density. Using the Van der Waals equation as an example, we explain how critical fluctuations lower the critical temperature, flatten the coexistence curve, induce a singularity in the isochoric heat capacity, and lead to apparent critical exponents that depend on the temperature distance from the critical point. [Copyright &y& Elsevier]

New experimental NMR data show that the unusual behavior, observed recently in the 35Cl NQR spectra, does not occur in 35Cl NMR measurements on BCPS. The results of the analysis of the 35Cl NMR line shape and the critical dynamics fit well with the predictions of the standard theory for IC systems. [ABSTRACT FROM AUTHOR]

Studies of the critical behavior of high-temperature superconductors (HTSC) show the importance of the strong doping dependence of the effective mass anisotropy γ for the generic ( T, x) phase diagram of these materials. A possible microscopic model that can explain the doping dependence of γ is based on polaronic charge carriers. That lattice effects may play a role for high-temperature superconductivity is further supported by measurements of the oxygen-isotope effect on the in-plane penetration depth λ ab(0) in underdoped La2− xSr xCuO4 single crystals that are reported in this paper. The oxygen-isotope effect on λ−2 ab(0) is found to be around −9% for the samples investigated. It arises mainly from the oxygen–mass dependence of the in-plane effective mass m* ab. The experimental facts presented in this paper suggest that lattice vibrations are important for the occurrence of high-temperature superconductivity. [ABSTRACT FROM AUTHOR]

Combining concepts of artificial neural networks (ANNs) with the stochastic dynamics of Ising spin lattices we introduce a hybrid model, the hybrid spin model (HSM). We find that the HSM carries the critical/tricritical fluctuations of the 2D Ising model and allows for an accurate estimation of the isothermal critical/tricritical exponents of 2D Ising universality class. Our work clearly demonstrates that HSM launches a new category of models supporting alternative pathways for the realization of criticality in complex networks artificial or real. [ABSTRACT FROM AUTHOR]