Weak Power Law Research Articles

Aperture size distribution, length, and preferential location of bed-parallel veins in shale

Bed-parallel, calcite-filled veins (BPVs) are common in shale formations, and although they have been widely described in other studies, little is known about their population aperture size distribution. To address this knowledge gap, we analyzed BPV sizes in outcrops and cores from the Vaca Muerta Formation, Neuquén Basin, Argentina; in two cores from the Marcellus Formation, Appalachian Basin, northeast Pennsylvania; and in one core from the Wolfcamp Shale, Delaware Basin, West Texas. Nine out of ten aperture size populations follow a negative exponential distribution, with one following a weak power law. Bed-parallel vein size distribution and intensity vary among formations and within the same shale. We define three groups of distributions: (1) Vaca Muerta outcrops, with the highest BPV intensity and the largest BPVs (cumulative frequency of 4.9 BPVs per meter [BPVs/m] for apertures 0.265 mm to 8.7 cm); (2) Vaca Muerta cores with a similar BPV intensity overall but with no apertures wider than 1.2 cm; and (3) Vaca Muerta, Wolfcamp, and Marcellus cores with the fewest BPVs (cumulative frequency up to 0.63 BPVs/m) and very few wider than 1 cm. Aperture and length in two outcrop data sets are weakly positively correlated and follow power laws with exponents of 0.44 and 0.49. Mechanical interfaces at boundaries between different lithologies exert a strong control on BPV location, with 65–75% of observed interfaces having BPVs along them. Only 25–30% of the BPVs occur at observed material interfaces, however, and unless subtle, unobserved mechanical layering is present, other factors must also control location. BPV intensity and organic richness (TOC) from Vaca Muerta well logs are correlated in some instances but not in others, indicating TOC is not always a good proxy for BPV location or intensity. These findings provide useful information for modeling of hydraulic fracture treatments where BPVs may influence development of the stimulated fracture network, for example by limiting height growth.

Approximate Nonlocal Symmetries for a Perturbed Schrödinger Equation with a Weak Infinite Power-Law Memory

A nonlocally perturbed linear Schrödinger equation with a small parameter was derived under the assumption of low-level fractionality by using one of the known general nonlocal wave equations with an infinite power-law memory. The problem of finding approximate symmetries for the equation is studied here. It has been shown that the perturbed Schrödinger equation inherits all symmetries of the classical linear equation. It has also been proven that approximate symmetries corresponding to Galilean transformations and projective transformations of the unperturbed equation are nonlocal. In addition, a special class of nonlinear, nonlocally perturbed Schrödinger equations that admits an approximate nonlocal extension of the Galilei group is derived. An example of constructing an approximately invariant solution for the linear equation using approximate scaling symmetry is presented.

Transitions and Origin of the Type-B Quasi-periodic Oscillations in the Black Hole X-Ray Binary MAXI J1348–630

The fast transitions between different types of quasi-periodic oscillations (QPOs) are generally observed in black hole transient sources (BHTs). We present a detailed study of the timing and spectral properties of the transitions of type-B QPOs in MAXI J1348–630, observed by Insight-HXMT. The fractional rms variability–energy relationship and energy spectra reveal that type-B QPOs probably originate from jet precession. Compared to a weak power-law dominated power spectrum, when type-B QPOs are present, the corresponding energy spectrum shows an increase in the Comptonization component and the need for the xillverCp component, and a slight increase in the height of the corona when using the relxilllp model. Therefore, we suggest that a coupled inner disk-jet region is responsible for the observed type-B QPO transitions. The timescale for the appearance/disappearance of type-B QPOs is either long or short (seconds), which may indicate instability of the disk-jet structure. For these phenomena, we hypothesize that the Bardeen–Petterson effect causes the disk-jet structure to align with the BH spin axis or that the disappearance of small-scale jets bound by the magnetic flux tubes leads to the disappearance of type-B QPOs. We observed three events regarding the B/C transitions, one of which occurred over a short time period from ∼9.2 Hz (C) to ∼4.8 Hz (B). The energy spectral analysis for the other two transitions shows that when type-C QPO is present, the Comptonization flux is higher, the spectrum is harder, and the inner radius of the disk changes insignificantly. We suggest that type-C QPOs probably originate from relatively stronger jets or the corona.

Intermittency of turbulent velocity and scalar fields using three-dimensional local averaging

An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $\theta$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_\lambda$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_\lambda$). The intermittency exponent of the energy dissipation rate is $\mu \approx 0.23$, whereas that of enstrophy is slightly larger; trends with $R_\lambda$ suggest that this will be the case even at extremely large $R_\lambda$. The intermittency exponent of the scalar dissipation rate is $\mu_\theta \approx 0.35$ for $Sc=1$. These findings are in essential agreement with previously reported results in the literature. We further show that $\mu_\theta$ decreases monotonically with increasing $Sc$, either as $1/\log Sc$ or a weak power law, suggesting that $\mu_\theta \to 0$ as $Sc \to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.

Revealing mobility pattern of taxi movements with its travel trajectory

Taxi movements contain much mobility information of passengers and taxi drivers in a city. However, previous researches often overlook the continuous movements of a single taxi. In this paper, we study the mobility pattern of taxi movements by analyzing the visiting sequences which record the cells (i.e., locations) being visited by taxis. At the collective level, we observe the weak power-law scaling exists in the relation between the number of visits of a cell and the corresponding number of taxis. At the individual level, we notice some unusual characteristics of continuous movements of a single taxi: (i) the number of different cells that have been visited increase with the visit number and shows a robust scaling behavior; (ii) the cell’s visiting frequency decreases with the rank of the cell and presents as a logarithm function; (iii) The distribution of the number of visits taken to revisit one cell presents as an exponential distribution. The empirical result demonstrates that the taxi movements do follow the unified pattern and show a stronger exploration tendency and weaker preferential return than other human dynamics. Finally, we utilize an agent-based model to reveal and understand the unified pattern of taxi movements. The model results indicate that the rank distribution is an intrinsic characteristic to explore the taxi destination choice and simulate the taxi movements.

Cell mechanical properties of human breast carcinoma cells depend on temperature

The knowledge of cell mechanics is required to understand cellular processes and functions, such as the movement of cells, and the development of tissue engineering in cancer therapy. Cell mechanical properties depend on a variety of factors, such as cellular environments, and may also rely on external factors, such as the ambient temperature. The impact of temperature on cell mechanics is not clearly understood. To explore the effect of temperature on cell mechanics, we employed magnetic tweezers to apply a force of 1 nN to 4.5 µm superparamagnetic beads. The beads were coated with fibronectin and coupled to human epithelial breast cancer cells, in particular MCF-7 and MDA-MB-231 cells. Cells were measured in a temperature range between 25 and 45 °C. The creep response of both cell types followed a weak power law. At all temperatures, the MDA-MB-231 cells were pronouncedly softer compared to the MCF-7 cells, whereas their fluidity was increased. However, with increasing temperature, the cells became significantly softer and more fluid. Since mechanical properties are manifested in the cell’s cytoskeletal structure and the paramagnetic beads are coupled through cell surface receptors linked to cytoskeletal structures, such as actin and myosin filaments as well as microtubules, the cells were probed with pharmacological drugs impacting the actin filament polymerization, such as Latrunculin A, the myosin filaments, such as Blebbistatin, and the microtubules, such as Demecolcine, during the magnetic tweezer measurements in the specific temperature range. Irrespective of pharmacological interventions, the creep response of cells followed a weak power law at all temperatures. Inhibition of the actin polymerization resulted in increased softness in both cell types and decreased fluidity exclusively in MDA-MB-231 cells. Blebbistatin had an effect on the compliance of MDA-MB-231 cells at lower temperatures, which was minor on the compliance MCF-7 cells. Microtubule inhibition affected the fluidity of MCF-7 cells but did not have a significant effect on the compliance of MCF-7 and MDA-MB-231 cells. In summary, with increasing temperature, the cells became significant softer with specific differences between the investigated drugs and cell lines.

Influence of thermal fluctuations on active diffusion at large Péclet numbers

Three-dimensional Wavelet Monte Carlo dynamics simulations are used to study the dynamics of passive particles in the presence of microswimmers—both represented by neutrally buoyant spheres—taking into account the often-omitted thermal motion alongside the hydrodynamic flows generated by the swimmers. Although the Péclet numbers considered are large, we find the thermal motion to have a significant effect on the dynamics of our passive particles and can be included as a decorrelation factor in the velocity autocorrelation with a decay time proportional to the Péclet number. Similar decorrelation factors come from swimmer rotations, e.g., run and tumble motion, and apply to both entrainment and far field loop contributions. These decorrelation factors lead to active diffusivity having a weak apparent power law close to Pe0.2 for small tracer-like particles at Péclet numbers appropriate for E. coli swimmers at room temperature. Meanwhile, the reduced hydrodynamic response of large particles to nearby forces has a corresponding reduction in active diffusivity in that regime. Together, they lead to a non-monotonic dependence of active diffusivity on particle size that can shed light on similar behavior observed in the experiments by Patteson et al. [“Particle diffusion in active fluids is non-monotonic in size,” Soft Matter 12, 2365–2372 (2016)].

Size distribution law of earthquake-triggered landslides in different seismic intensity zones

Abstract. The Ms 8.0 Wenchuan earthquake in 2008 and Ms 7.0 Lushan earthquake in 2013 produced thousands of landslides in the southern region of the Longmen Mountains in China. We conducted field investigations and analyzed remote sensing data to determine the distribution law of earthquake-triggered landslides. The results show a strong negative power law relationship between the size and frequency of landslides in VII, VIII, and IX seismic intensity zones, a weak power law in the X seismic intensity zone, and a lognormal distribution in the XI seismic intensity zone. Landslide density increases with increasing seismic intensity. A sandpile cellular automata model was built under the conceptual framework of self-organized criticality theory to simulate earthquake-induced landslides. Data from the simulations demonstrate that, with increasing disturbance intensity, the dynamical mechanism of the sandpile model changes from a strong power law to a weak power law and then to a lognormal distribution. Results from shaking table experiments of a one-sided slope sandpile show that, for peak ground acceleration (PGA) in the range of 0.075–0.125 g, the relation between the amount and frequency of sand follows a negative power law. For PGA between 0.15 and 0.25 g, the relation obeys a lognormal distribution. This verifies that the abovementioned distribution of earthquake-induced landslides should be a universal law from a physical viewpoint and may apply to other areas. This new perspective may be used to guide the development of an inventory of earthquake-triggered landslides and provide a scientific basis for their prediction.

Measuring (biological) materials mechanics with atomic force microscopy. 2. Influence of the loading rate and applied force (colloidal particles)

Atomic force microscopy (AFM) is the most often used tool to study the mechanical properties of eukaryotic cells. Due to their complex assembly, cells show viscoelastic properties. When performing experiments, one has to consider the influence of both loading rate and maximum load on the measured mechanical properties. Here, we employed colloidal particles of various sizes (from 2 to 20 μm diameter) to perform force spectroscopy measurements on endothelial cells at loading rates varying from 0.1 to 50 μm/s, and maximum loads ranging from 1 to 25 nN. We were able to determine the non-linear dependence of cell viscoelastic properties on the loading rate which followed a weak power law. In addition, we show that previous loading at high forces leads to a stiffening of cells. Based on these results we discuss a road map for determining cell mechanical properties using AFM. Finally, this work provides an experimental framework for cell mechanical measurements using force-cycle experiments.

Environmentally controlled magnetic nano-tweezer for living cells and extracellular matrices

The magnetic tweezer technique has become a versatile tool for unfolding or folding of individual molecules, mainly DNA. In addition to single molecule analysis, the magnetic tweezer can be used to analyze the mechanical properties of cells and extracellular matrices. We have established a magnetic tweezer that is capable of measuring the linear and non-linear viscoelastic behavior of a wide range of soft matter in precisely controlled environmental conditions, such as temperature, CO2 and humidity. The magnetic tweezer presented in this study is suitable to detect specific differences in the mechanical properties of different cell lines, such as human breast cancer cells and mouse embryonic fibroblasts, as well as collagen matrices of distinct concentrations in the presence and absence of fibronectin crosslinks. The precise calibration and control mechanism employed in the presented magnetic tweezer setup provides the ability to apply physiological force up to 5 nN on 4.5 µm superparamagnetic beads coated with fibronectin and coupled to the cells or collagen matrices. These measurements reveal specific local linear and non-linear viscoelastic behavior of the investigated samples. The viscoelastic response of cells and collagen matrices to the force application is best described by a weak power law behavior. Our results demonstrate that the stress stiffening response and the fluidization of cells is cell type specific and varies largely between differently invasive and aggressive cancer cells. Finally, we showed that the viscoelastic behavior of collagen matrices with and without fibronectin crosslinks measured by the magnetic tweezer can be related to the microstructure of these matrices.

Force-induced gene up-regulation does not follow the weak power law but depends on H3K9 demethylation.

Mechanical forces play important roles in development, physiology, and diseases, but how force is transduced into gene transcription remains elusive. Here, we show that transcription of transgene DHFR or endogenous genes egr-1 and Cav1 is rapidly up-regulated in response to cyclic forces applied via integrins at low frequencies but not at 100 Hz. Gene up-regulation does not follow the weak power law with force frequency. Force-induced transcription up-regulation at the nuclear interior is associated with demethylation of histone H3 lysine-9 trimethylation (H3K9me3), whereas no transcription up-regulation near the nuclear periphery is associated with H3K9me3 that inhibits Pol II recruitment to the promoter site. H3K9me3 demethylation induces Pol II recruitment and increases force-induced transcription of egr-1 and Cav1 at the nuclear interior and activates mechano-nonresponsive gene FKBP5 near the nuclear periphery, whereas H3K9me3 hypermethylation has opposite effects. Our findings demonstrate that rapid up-regulation of endogenous mechanoresponsive genes depends on H3K9me3 demethylation.

Single-molecule lamellar hydrogels from bolaform microbial glucolipids.

Lipid lamellar hydrogels are rare soft fluids composed of a phospholipid lamellar phase instead of fibrillar networks. The mechanical properties of these materials are controlled by defects, induced by local accumulation of a polymer or surfactant in a classical lipid bilayer. Herein we report a new class of lipid lamellar hydrogels composed of one single bolaform glycosylated lipid obtained by fermentation. The lipid is self-organized into flat interdigitated membranes, stabilized by electrostatic repulsive forces and stacked in micrometer-sized lamellar domains. The defects in the membranes and the interconnection of the lamellar domains are responsible, from the nano- to the micrometer scales, for the elastic properties of the hydrogels. The lamellar structure is probed by combining small angle X-ray and neutron scattering (SAXS, SANS), the defect-rich lamellar domains are visualized by polarized light microscopy while the elastic properties are studied by oscillatory rheology. The latter show that both storage G' and loss G'' moduli scale as a weak power-law of the frequency, that can be fitted with fractional rheology models. The hydrogels possess rheo-thinning properties with second-scale recovery. We also show that ionic strength is not only necessary, as one could expect, to control the interactions in the lamellar phase but, most importantly, it directly controls the elastic properties of the lamellar gels.

Probing Fluctuations and Avalanches in the Cytoskeleton with Active Micropost Arrays

The cellular actomyosin network plays an important role in a wide range of cell behavior, including motility, morphology and mechanotransduction. Although the building blocks of actomyosin networks are well understood at the molecular level, the picture connecting these microscale units to cell-scale behavior remains incomplete. Here we present results using active micropost array detectors (AMPADS) to characterize the dynamical fluctuations and local rheology of cellular actomyosin networks in detail. AMPADS are poly(dimethylsiloxane) (PDMS) micropillar arrays with embedded magnetic nanowires that enable mechanical actuation of an adherent cell. We classified the cell-associated microposts based on their traction force, and identified two distinct populations, one containing posts coupled to stress fibers and the other containg posts coupled to the actomyosin cortex. Both groups show weak power law rheology, but we find that the fluctuations of stress fiber-associated posts are more active and highly anisotropic in comparison to the cortically-associated posts. Notably, the fluctuations of both populations are highly heterogenous and resemble a Lévy process. Specifically, the mean-squared displacements of both types of posts display broadly distributed amplitudes and super-diffusive behavior. We find that the amplitude distribution is fat-tailed, and is dominated by a corresponding distribution of intermittent, large step-like displacements, resembling avalanches and earthquakes in physical systems. Our regular array of detectors also allows us to determine the spatial extent and average symmetry of the largest rearrangements in the cortex, which are both spatially and temporally complex, resembling those in plastic solids. These results suggest that the dynamics of the cellular actomyosin network resembles what is seen in soft matter systems such as sandpiles and foams, where constituent components self-organize into marginally stable, plastic networks, with significant implications for future models of the cortex.

Superconductivity in doped FeTe1−xSx (x = 0.00 to 0.25) single crystals

We report self flux growth and characterization of FeTe1-xSx (x = 0.00 to 0.25) single crystal series. Surface x-ray diffraction (XRD) exhibited crystalline nature with growth in (00l) plane. Micro-structural (electron microscopy) images of representative crystals showed the slab-like morphology and near stoichiometric composition. Powder XRD analysis (Rietveld) of single crystals exhibited tetragonal structure with P4/nmm space group and decreasing a and c lattice parameters with increase in x. Electrical resistivity measurements (ρ-T) showed superconductivity with at 9.5 K and 8.5 K for x = 0.10 and x = 0.25 respectively. The un-doped crystal, i.e., x = 0.00, exhibited known step like anomaly at around 70 K. Upper critical field Hc2(0), as calculated from magneto transport [ρ(T)H], for x = 0.25 crystal is around 60Tesla and 45Tesla in H//ab and H//c directions. Thermal activation energy [U0(H)] calculated for x = 0.10 and 0.25 crystals followed weak power law, indicating single vortex pinning at low fields. Mossbauer spectra for FeTe1-xSx crystals at 300 K and 5 K are compared with non superconducting FeTe. Both quadrupole splitting (QS) and isomer shift (IS) for S doped crystals were found to decrease. Also at 5 K the hyperfine field for x = 0.10 superconducting crystal is decreased substantially from 10.6Tesla (FeTe) to 7.2Tesla. For x = 0.25 crystal, though small quantity of un-reacted Fe is visible at room temperature, but unlike x = 0.10, the low temperature (5 K) ordered FeTe hyperfine field is nearly zero.

Multiwavelength follow-up observations of the tidal disruption event candidate 2XMMi J184725.1−631724

The ultrasoft X-ray flare 2XMMi J184725.1-631724 was serendipitously detected in two XMM-Newton observations in 2006 and 2007, with a peak luminosity of 6X10^43 erg/s. It was suggested to be a tidal disruption event (TDE) because its position is consistent with the center of an inactive galaxy. It is the only known X-ray TDE candidate whose X-ray spectra showed evidence of a weak steep powerlaw component besides a dominant supersoft thermal disk. We have carried out multiwavelength follow-up observations of the event. Multiple X-ray monitorings show that the X-ray luminosity has decayed significantly after 2011. Especially, in our deep Chandra observation in 2013, we detected a very faint counterpart that supports the nuclear origin of 2XMMi J184725.1-631724 but had an X-ray flux a factor of ~1000 lower than in the peak of the event. Compared with follow-up UV observations, we found that there might be some enhanced UV emission associated with the TDE in the first XMM-Newton observation. We also obtained a high-quality UV-optical spectrum with the SOAR and put a very tight constraint on the persistent nuclear activity, with a persistent X-ray luminosity expected to be lower than the peak of the flare by a factor of >2700. Therefore, our multiwavelength follow-up observations strongly support the TDE explanation of the event.

Nearly Constant Loss (NCL) in Lithium Metasilicate Glass at Low Temperatures—Anisotropic and Dynamical Caging from Molecular Dynamics Simulations

Ions in ionically conducting materials show complex but universal trends in the time development of the mean squared displacements (MSD) of ions, which correspond to the complex frequency dependence conductivity spectra or susceptibility. Molecular dynamics simulations enable us to characterize the details of such motions including the initial nearly logarithmic or weak power law time dependence of the MSD of caged ions, showing up in susceptibility as the nearly constant loss (NCL) and the important connections of the caged ion dynamics to ion hopping dynamics in ionically conducting materials. In previous works, the motion of ions in the NCL region for lithium metasilicate was characterized at 700 and 500 K. Since each time region of MSD becomes longer and longer with decreasing temperature, the NCL region will cover the entire observation time during the MD run at lower temperatures, and thus enabling a more detailed study of the properties of the NCL. This paper reports results from new simulations at...

Ocean swell within the kinetic equation for water waves

Abstract. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2 × 106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height) due to wave–wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell). At longer times, wave–wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar) data. At the same time, the relatively fast weakening of wave–wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.

Viscoelastic Properties of Confluent MDCK II Cells Obtained from Force Cycle Experiments

The local mechanical properties of cells are frequently probed by force indentation experiments carried out with an atomic force microscope. Application of common contact models provides a single parameter, the Young’s modulus, to describe the elastic properties of cells. The viscoelastic response of cells, however, is generally measured in separate microrheological experiments that provide complex shear moduli as a function of time or frequency. Here, we present a straightforward way to obtain rheological properties of cells from regular force distance curves collected in typical force indentation measurements. The method allows us to record the stress-strain relationship as well as changes in the weak power law of the viscoelastic moduli. We derive an analytical function based on the elastic-viscoelastic correspondence principle applied to Hertzian contact mechanics to model both indentation and retraction curves. Rheological properties are described by standard viscoelastic models and the paradigmatic weak power law found to interpret the viscoelastic properties of living cells best. We compare our method with atomic force microscopy-based active oscillatory microrheology and show that the method to determine the power law coefficient is robust against drift and largely independent of the indentation depth and indenter geometry. Cells were subject to Cytochalasin D treatment to provoke a drastic change in the power law coefficient and to demonstrate the feasibility of the approach to capture rheological changes extremely fast and precisely. The method is easily adaptable to different indenter geometries and acquires viscoelastic data with high spatiotemporal resolution.

Simultaneous Rheoelectric Measurements of Strongly Conductive Complex Fluids

We introduce a novel apparatus designed for stress-controlled rheometers to perform simultaneous rheological and electrical measurements on strongly conductive complex fluids under shear. By means of a non-toxic liquid metal at room temperature, the electrical connection to the rotating shaft is completed with minimal additional mechanical friction, allowing for simultaneous stress measurements as low as 1 Pa. We use the capabilities of this design to perform an extensive set of rheo-electric experiments on gels formulated from attractive carbon black particles, at concentrations ranging from 4 to 15% wt. First, experiments on gels at rest prepared with different shear history show a robust power-law scaling between the elastic modulus $G'_0$ and the conductivity $\sigma_0$ of the gels, i.e. $G'_0 \sim \sigma_0^\alpha$, with $\alpha =1.65 \pm 0.04$ independently of the gel concentration. Second, conductivity measurements performed simultaneously with creep experiments reveal for the first time that plastic events take place in the bulk while the shear rate decreases as a weak power law of time in the early stage of the experiment. The subsequent evolution of the conductivity and shear rate allows us to propose a local yielding scenario that is in agreement with previous velocimetry measurements. Finally, we determine the constitutive rheological and electrical behavior of carbon black gels. Corrections first introduced for mechanical measurements are carefully extended to electrical measurements to accurately distinguish between bulk and surface contributions to the conductivity. As an illustrative example, we examine the constitutive rheo-electric properties of five carbon black gels of different grades, and demonstrate the relevance of the novel rheo-electric apparatus as a versatile characterization tool for strongly conductive complex fluids and their applications.

Brittle-to-quasibrittle transition in bundles of nonlinear elastic fibers.

Properties of the fiber bundle model have been studied using equal load-sharing dynamics where each fiber obeys a nonlinear stress (s)-strain (x) characteristic function s=G(x) till its breaking threshold. In particular, four different functional forms have been studied: G(x)=e^{αx},1+x^{α},x^{α}, and xe^{αx} where α is a continuously tunable parameter of the model in all cases. Analytical studies, supported by extensive numerical calculations of this model, exhibit a brittle to quasibrittle phase transition at a critical value of α_{c} only in the first two cases. This transition is characterized by the weak power law modulated logarithmic (brittle) and logarithmic (quasibrittle) dependence of the relaxation time on the two sides of the critical point. Moreover, the critical load σ_{c}(α) for the global failure of the bundle depends explicitly on α in all cases. In addition, four more cases have also been studied, where either the nonlinear functional form or the probability distribution of breaking thresholds has been suitably modified. In all these cases similar brittle to quasibrittle transitions have been observed.