Power-law Characteristics Research Articles

Decay of Fermionic Quasiparticles in One-Dimensional Quantum Liquids

The low-energy properties of one-dimensional quantum liquids are commonly described in terms of the Tomonaga-Luttinger liquid theory, in which the elementary excitations are free bosons. To this approximation, the theory can be alternatively recast in terms of free fermions. In both approaches, small perturbations give rise to finite lifetimes of excitations. We evaluate the decay rate of fermionic excitations and show that it scales as the eighth power of energy, in contrast to the much faster decay of bosonic excitations. Our results can be tested experimentally by measuring the broadening of power-law features in the density structure factor or spectral functions.

Spin turbulence with small spin magnitude in spin-1 spinor Bose-Einstein condensates

We theoretically and numerically study spin turbulence (ST) with small spin magnitude in spin-1 spinor Bose-Einstein condensates by using the spin-1 spinor Gross-Pitaevskii (GP)equations. This kind of ST is realized in two cases: (i) with antiferromagnetic interaction and (ii) with ferromagnetic interaction under a static magnetic field. The ST with small spin magnitude can exhibit two characteristic power laws in the spectrum of the spin-dependent interaction energy: -1 and -7/3 power laws in the low- and high-wave-number regions, respectively. These power laws are derived from a Kolmogorov-type dimensional scaling analysis for the equations of motion of the spin vector and nematic tensor. To confirm these power laws, we perform a numerical calculation of the spin-1 spinor GP equations in a two-dimensional uniform system. In case (i), the -7/3 power law appears in the high-wave-number region, but the spectrum in the low-wave-number region deviates from the -1 power law. In contrast, both -1 and -7/3 power laws are found to clearly appear in case (ii).

The Snakelike Chain Character of Unstructured RNA

In the absence of base-pairing and tertiary structure, ribonucleic acid (RNA) assumes a random-walk conformation, modulated by the electrostatic self-repulsion of the charged, flexible backbone. This behavior is often modeled as a Kratky-Porod “wormlike chain” (WLC) with a Barrat-Joanny scale-dependent persistence length. In this study we report measurements of the end-to-end extension of poly(U) RNA under 0.1 to 10 pN applied force and observe two distinct elastic-response regimes: a low-force, power-law regime characteristic of a chain of swollen blobs on long length scales and a high-force, salt-valence-dependent regime consistent with ion-stabilized crumpling on short length scales. This short-scale structure is additionally supported by force- and salt-dependent quantification of the RNA ion atmosphere composition, which shows that ions are liberated under stretching; the number of ions liberated increases with increasing bulk salt concentration. Both this result and the observation of two elastic-response regimes directly contradict the WLC model, which predicts a single elastic regime across all forces and, when accounting for scale-dependent persistence length, the opposite trend in ion release with salt concentration. We conclude that RNA is better described as a “snakelike chain,” characterized by smooth bending on long length scales and ion-stabilized crumpling on short length scales. In monovalent salt, these two regimes are separated by a characteristic length that scales with the Debye screening length, highlighting the determining importance of electrostatics in RNA conformation.

Fading Signatures of Critical Brain Dynamics during Sustained Wakefulness in Humans

Sleep encompasses approximately a third of our lifetime, yet its purpose and biological function are not well understood. Without sleep optimal brain functioning such as responsiveness to stimuli, information processing, or learning may be impaired. Such observations suggest that sleep plays a crucial role in organizing or reorganizing neuronal networks of the brain toward states where information processing is optimized. Increasing evidence suggests that cortical neuronal networks operate near a critical state characterized by balanced activity patterns, which supports optimal information processing. However, it remains unknown whether critical dynamics is affected in the course of wake and sleep, which would also impact information processing. Here, we show that signatures of criticality are progressively disturbed during wake and restored by sleep. We demonstrate that the precise power-laws governing the cascading activity of neuronal avalanches and the distribution of phase-lock intervals in human electroencephalographic recordings are increasingly disarranged during sustained wakefulness. These changes are accompanied by a decrease in variability of synchronization. Interpreted in the context of a critical branching process, these seemingly different findings indicate a decline of balanced activity and progressive distance from criticality toward states characterized by an imbalance toward excitation where larger events prevail dynamics. Conversely, sleep restores the critical state resulting in recovered power-law characteristics in activity and variability of synchronization. These findings support the intriguing hypothesis that sleep may be important to reorganize cortical network dynamics to a critical state thereby assuring optimal computational capabilities for the following time awake.

PMMA/Polysaccharides Nanofilm Loaded with Adenosine Deaminase Inhibitor for Targeted Anti-inflammatory Drug Delivery

A novel drug delivery vector, a free-standing polymeric ultrathin film (nanofilm) composed of PMMA and a polysaccharides multilayer, is presented. Chitosan and sodium alginate are alternatively deposited by spin-assisted LbL assembly onto a plasma-treated PMMA thin film. Hydrophobic anti-inflammatory drugs, an adenosine deaminase inhibitor (APP) and its fluorescent dansyl derivate (APP-Dns), are encapsulated inside the LbL multilayer using a simple casting deposition procedure. The resulting drug loaded nanofilm can be suspended in water upon dissolution of a PVA sacrificial layer. Morphological characterization of the nanofilm shows that PMMA/LbL nanofilms possess nanometric thickness (<200 nm) and very low surface roughness (1-2 nm for drug loaded nanofilms and <1 nm for blank nanofilm). Drug loaded films exhibit a diffusion controlled release mechanism following the Korsmayer-Peppas release model, confirmed by the fit of release data with a characteristic power law. Drug release is impaired through the PMMA layer, which acts effectively as a barrier for drug transport. This ultrathin polymer film can find application as a nanopatch for targeted inflammatory drug delivery to treat localized pathologies as inflammatory bowel disease.

Radiative transfer theory for the fractal structure and power-law decay characteristics of short-period seismograms

Radiative transfer theory for the fractal structure and power-law decay characteristics of short-period seismograms

Iso-Frictional Mass Dependence of Diffusion of Polymer Melts Revealed by1H NMR Relaxometry

We extract the translational diffusion coefficient D(T,M) from field cycling (FC) 1H NMR relaxometry which provides the relaxation dispersion of poly(dimethylsiloxane), 1,4-poly(butadiene), poly(styrene), 1,4-poly(isoprene), and poly(propylene glycol) with various molecular masses M. Oligomers with very low M, nonentangled (M < Me), and entangled (M > Me) polymers are included. The low-frequency 1H NMR relaxation dispersion is dominated by translational dynamics and allows extracting D via benefiting from an universal dispersion power-law characteristic of free diffusion. In order to correct for the additional mass dependence of the monomeric friction coefficient observed at low M and controlled by the M dependence of the glass transition, the segmental correlation time τs(T,M) is taken from previous analyses of the FC susceptibility master curves. Consequently, we present the temperature independent, iso-frictional quantity Dτs ∝ F(M), which reveals the M-dependence of the pure collective polymer dynamics. While at the lowest M the quantity Dτs displays a trend to become M independent typical of simple liquids, it crosses over to a behavior characteristic of Rouse dynamics. In most systems, however, this crossover manifests itself in a rather narrow M interval as entanglement dynamics takes over at M > Me. Thus, pure Rouse behavior is difficult to identify, yet the approach allows one to decide when a molecule becomes a polymer, in terms of the (smallest) Rouse unit.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

On the power-law pressure dependence of the plastic strain rate of crystals under intense shock wave loading

The plastic deformation of metallic crystals under intense shock wave loading has been theoretically investigated. It has been experimentally found that the plastic strain rate \(\dot \varepsilon \) and the pressure in the wave P are related by the empirical expression \(\dot \varepsilon \) ∼ P4 (the Swegle-Grady law). The performed dislocation-kinetic analysis of the mechanism of the origin of this relationship has revealed that its power-law character is determined by the power-law pressure dependence of the density of geometrically necessary dislocations generated at the shock wave front ρ ∼ P3. In combination with the rate of viscous motion of dislocations, which varies linearly with pressure (u ∼ P), this leads to the experimentally observed relationship \(\dot \varepsilon \) ∼ P4 for a wide variety of materials with different types of crystal lattices in accordance with the Orowan relationship for the plastic strain rate \(\dot \varepsilon \) = bρu (where b is the Burgers vector). In the framework of the unified dislocation-kinetic approach, it has been theoretically demonstrated that the dependence of the pressure (flow stress) on the plastic strain rate over a wide range from 10−4 to 1010 s−1 reflects three successively developing processes: the thermally activated motion of dislocations, the viscous drag of dislocations, and the generation of geometrically necessary dislocations at the shock wave front.

Analytical Methods and Formulas for Modeling High Temperature Superconductors

The electrodynamics of type-II superconductors is considered in the quasi-static limit when the concept of the so-called critical state is well applicable to the superconductors. We review analytical techniques and formulas used to describe the critical states in the superconductors of the various shapes characteristic of high-temperature superconducting materials. In particular, it is explained how 3-D critical-state problems for thin planar superconductors can be reduced to more simple 2-D problems. Within this approach, the critical states in a thin infinitely long superconducting strip are analytically described not only in the simplest case of a constant critical current density jc but also in the case of anisotropic flux-line pinning and for simple model dependence of jc on the magnetic-field magnitude. We also present the analytical solutions of the critical-state problem for superconducting strips with ferromagnetic substrates and for various arrays of superconducting strips with a transport current or in an external magnetic field. In particular, one of the discussed configurations of the strips can model superconducting power transmission cables. We also describe some analytical solutions of the electrodynamic equations for type-II superconductors with power-law voltage-current characteristics.

Spectral properties of keV-energetic ion populations inside the heliopause reflected by IBEX-relevant energetic neutral atoms

For more than three years now, the IBEX mission monitors fluxes of energetic neutral atoms (ENAs) in the range between 0.1 to 6 keV from all directions of the sky. During this extended observation period, it could be confirmed that an outstanding ENA emission feature, called the “ribbon”, has been continuously found over the past years. In addition, spectral flux features also have become the target of refined observations. In this study, we thus aim at delivering theoretically calculated results on spectral ENA flux properties. The ENAs we are considering in this paper are due to two types of transcharged pick-up ions present in the heliosheath region: primary pick-up ions that have been energetically processed at their passage over the termination shock, and ions induced to the pick-up ion regime from adiabatically cooled anomalous cosmic ray ions. Both components have different spectra, so we need to consider ENA fluxes generated by charge-exchange processes from the superposed distributions of these two populations. We derive the spectral features of ENA fluxes along a line-of-sight as a function of the celestial direction and compare them with IBEX observations. The power-law characteristics of the resulting spectra exhibit a good match with the average power indices observed by IBEX in large sections of the heliosphere, with the notable exception of the heliotail, for which our adopted heliospheric model does not provide an accurate enough representation.

Power law statistics of rippled graphene nanoflakes

Graphene nanoflakes (GNFs) are predicted to possess novel magnetic, optical, and spintronic properties. They have recently been synthesized and a number of applications are being studied. Here we investigate the statistical properties of rippled GNFs (50–5,000 atoms) at $$\text{ T}=300$$ K. An adjacency matrix is calculated from the coordinates and we find that the free energy, enthalpy, entropy, and atomic displacement all show power law behavior. The vibrational energy versus the Wiener index also shows power law character. We distinguish between using Euclidean topographical indices and compare them to topological ones. These properties are determined from atomic coordinates using MATLAB routines.

Understanding human dynamics in microblog posting activities

Human activity patterns are an important issue in behavior dynamics research. Empirical evidence indicates that human activity patterns can be characterized by a heavy-tailed inter-event time distribution. However, most researchers give an understanding by only modeling the power-law feature of the inter-event time distribution, and those overlooked non-power-law features are likely to be nontrivial. In this work, we propose a behavior dynamics model, called the finite memory model, in which humans adaptively change their activity rates based on a finite memory of recent activities, which is driven by inherent individual interest. Theoretical analysis shows a finite memory model can properly explain various heavy-tailed inter-event time distributions, including a regular power law and some non-power-law deviations. To validate the model, we carry out an empirical study based on microblogging activity from thousands of microbloggers in the Celebrity Hall of the Sina microblog. The results show further that the model is reasonably effective. We conclude that finite memory is an effective dynamics element to describe the heavy-tailed human activity pattern.

Structure properties of evolutionary spatially embedded networks

Abstract This work is a modeling of evolutionary networks embedded in one or two dimensional configuration space. The evolution is based on two attachments depending on degree and spatial distance. The probability for a new node n to connect with a previous node i at distance r n i follows a k i ∑ j k j + ( 1 − a ) r n i − α ∑ j r n j − α , where k i is the degree of node i , α and a are tunable parameters. In spatial driven model ( a = 0 ), the spatial distance distribution follows the power-law feature. The mean topological distance l and the clustering coefficient C exhibit phase transitions at same critical values of α which change with the dimensionality d of the embedding space. When a ≠ 0 , the degree distribution follows the “shifted power law” (SPL) which interpolates between exponential and scale-free distributions depending on the value of a .

Thoughts about thinking: cognition according to the second law of thermodynamics

A holistic account of the human brain is provided by the Second Law of Thermodynamics. According to this universal precept, the central nervous system is governed by the quest to consume free energy in the least possible time. The brain is like any other system of nature that has evolved over eons and continues to develop over an individual’s life time. This physical portrayal is singularly appropriate because power-law characteristics as well as oscillatory and at times unpredictable functioning are not exclusive attributes of the brain but are found in other systems throughout nature. The neural network comprises pathways for signal propagation just as other natural systems have pathways for the transmission of energy in various forms. These universalities support the view of the evolution and development of the human brain as a natural thermodynamic process. In a like manner perception, sensation and learning as well as the processes of memory, emotions and consciousness can be regarded as natural expressions of the neural network under the suzerainty of the Second Law. The outcomes of cognitive processes, like other natural processes, are non-deterministic because the interactive effects of flows of energy as signals with differences in energy as their driving forces cannot be separated from each other. This naturalistic framework also provides insight into mental disorders and cognitive defects.

Subdiffusive transport of fractional two-headed molecular motor

Focusing on the directed transport phenomena of the two-headed molecular motor, we adopt power function as the damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells and present the model of fractional coupling Brownian motor in overdamped condition in this paper. We also discuss the influences of fractional order and coupling factor on the transport speed. From the simulation results there are found the directed transport phenomena and the inverse transport which is not seen in the conventional Brownian motor, in the overdamped fractional coupling Brownian motor. When the noise density is fixed, the generalized stochastic resonance appears when transport speed varies with the fractional order and coupling factor. In particular, the results reveal that the magnitude and direction of the directional flow are controlled by coupling the noise with the interaction force between the two heads, which is the movement characteristic of the two-headed molecular motor in the memory ratchet, rather than of the single-headed motor.

Segmenting sign language into motor primitives with Bayesian binning.

The endpoint trajectories of human movements fulfill characteristic power laws linking velocity and curvature. The parameters of these power laws typically vary between different segments of longer action sequences. These parameters might thus be exploited for the unsupervised segmentation of actions into movement primitives. For the example of sign language we investigate whether such segments can be identified by Bayesian binning (BB), using a Gaussian observation model whose mean has a polynomial time dependence. We show that this method yields good segmentation and correctly models ground truth kinematics composed of consecutive segments derived from wrist trajectories recorded from users of Israeli Sign Language (ISL). Importantly, polynomial orders between 3 and 5 yield an optimal trade-off between complexity and accuracy of the trajectory approximation, in accordance with the minimum acceleration and minimum jerk models. Comparing the orders of the polynomials best approximating natural kinematics against those needed to fit the power law ground truth data suggests that kinematic properties not compatible with power laws are also not adequately represented by low order polynomials and require higher order polynomials for a good approximation.

Correlation between Shear Wave Velocity and Porosity in Porous Solids and Rocks

The shear wave velocity dependence on porosity was modelled using percolation theory model for the shear modulus porosity dependence. The obtained model is not a power law dependence (no simple scaling with porosity), but a more complex equation. Control parameters of this equation are shear wave velocity of bulk solid, percolation threshold of the material and the characteristic power law exponent for shear modulus porosity dependence. This model is suitable for all porous materials, mortars and porous rocks filled with liquid or gas. In the case of pores filled with gas the model can be further simplified: The term for the ratio of the gas density to the density of solid material can be omitted in the denominator (the ratio is usually in the range of (10−4, 10−3) for all solids). This simplified equation was then tested on the experimental data set for porous ZnO filled with air. Due to lack of reasonable data the scientists are encouraged to test the validity of proposed model using their experimental data.

Signatures of the superfluid to Mott insulator transition in equilibrium and in dynamical ramps

We investigate the equilibrium and dynamical properties of the Bose-Hubbard model and the related particle-hole symmetric spin-1 model in the vicinity of the superfluid to Mott insulator quantum phase transition. We employ the following methods: exact-diagonalization, mean-field (Gutzwiller), cluster mean-field, and mean-field plus Gaussian fluctuations. In the first part of the paper we benchmark the four methods by analyzing the equilibrium problem and give numerical estimates for observables such as the density of double occupancies and their correlation function. In the second part, we study parametric ramps from the superfluid to the Mott insulator and map out the crossover from the regime of fast ramps, which is dominated by local physics, to the regime of slow ramps with a characteristic universal power law scaling, which is dominated by long wavelength excitations. We calculate values of several relevant physical observables, characteristic time scales, and an optimal protocol needed for observing universal scaling.

Transient photoconductivity responses in amorphous In-Ga-Zn-O films

We studied the photoconductivity responses in amorphous In-Ga-Zn-O (a-IGZO) films using a time-resolved microwave photoconductivity decay (μ-PCD) technique. The a-IGZO film characteristics are correlated with three components in the photoconductivity response: the peak value and two decay constants. The peak value originated from the density of the photo-generated free carriers through carrier generation and recombination processes during laser pulse irradiation. Power law characteristics indicated that the peak values are attributed to recombination process related to the exponential distribution of the conduction band tail states. After the laser pulse was turned off, the reflectivity signal decreased rapidly, indicating fast recombination of the photo-generated carriers. This fast decay component is suggested to be related to the recombination processes through the deep level states. Following the fast decay, a slow decay with a decay constant on the order of microseconds appeared. This slow decay was attributed to the reemission of trapped carriers with an activation energy of ∼0.2 eV. In addition, both the fast and slow decays for the wet annealed a-IGZO film were longer than those of the as-deposited a-IGZO film. The decay constants are considered to reflect the density of the subgap states that act as trapping or recombination centers. The μ-PCD method provides a useful estimation of the film quality, such as the density of the defect states, and the physical properties of electronic devices using a-IGZO films.