Analyses of defect distributions in ZnO varistors based on the Jonscher’s universal power law and the Dissado–Hill model

The defect distributions in ZnO varistors mixed with Bi2O3, NiO, MnCO3, Co2O3, and SiO2 after doping Sb2O3 were investigated, based on the Jonscher’s universal power law and the Dissado–Hill model. The microstructures were investigated using x-ray diffractometer, scanning electron microscope, energy dispersive spectrometer, and x-ray photoelectron spectrometer. The capacitance–voltage (C–V) method was utilized to obtain the parameters of the double Schottky barrier. The dielectric spectra were analyzed to extract the parameters of defect distribution. The current density–electric field (J–E) characteristics were measured to obtain the parameters of electrical properties. We found that with increasing Sb2O3 content, the ZnO grain size distribution become more homogeneous in the Sb2O3-doped ZnO varistors; the density Zn i × is decreased; except for less homogeneous V O × , more homogeneous distributions of Zn i ∙ in the depletion layers and the extrinsic defects at the interfaces are achieved in the Sb2O3-doped ZnO varistors. Therefore, the enhancement in the electrical properties was achieved by doping Sb2O3 due to the increased number of active grain boundaries per unit volume, i.e. the increased breakdown field and nonlinear coefficient, and the decreased leakage current density. The results of this study suggest that the Jonscher’s universal power law and the Dissado–Hill model can be effectively used to analyze defect distributions in varistor ceramics.

A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells

Living cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

Maximal modularity and the optimal size of parliaments

An important question in representative democracies is how to determine the optimal parliament size of a given country. According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with an exponent equal to 1/3, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. In this work, we analyse this intriguing regularity using tools from complex networks theory. We model the population of a democratic country as a random network, drawn from a growth model, where each node is assigned a constituency membership sampled from an available set of size D. We calculate analytically the modularity of the population and find that its functional relation with the number of constituencies is strongly non-monotonic, exhibiting a maximum that depends on the population size. The criterion of maximal modularity allows us to predict that the number of representatives should scale as a power-law in the size of the population, a finding that is qualitatively confirmed by the empirical analysis of real-world data.

Universal statistics of vortices in a newborn holographic superconductor: beyond the Kibble-Zurek mechanism

Traversing a continuous phase transition at a finite rate leads to the breakdown of adiabatic dynamics and the formation of topological defects, as predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate universal signatures beyond the KZM, by characterizing the distribution of vortices generated in a thermal quench leading to the formation of a holographic superconductor. The full counting statistics of vortices is described by a binomial distribution, in which the mean value is dictated by the KZM and higher-order cumulants share the universal power-law scaling with the quench time. Extreme events associated with large fluctuations no longer exhibit a power-law behavior with the quench time and are characterized by a universal form of the Weibull distribution for different quench rates.

Conformal Floquet dynamics with a continuous drive protocol

We study the properties of a conformal field theory (CFT) driven periodically with a continuous protocol characterized by a frequency ωD. Such a drive, in contrast to its discrete counterparts (such as square pulses or periodic kicks), does not admit exact analytical solution for the evolution operator U. In this work, we develop a Floquet perturbation theory which provides an analytic, albeit perturbative, result for U that matches exact numerics in the large drive amplitude limit. We find that the drive yields the well-known heating (hyperbolic) and non-heating (elliptic) phases separated by transition lines (parabolic phase boundary). Using this and starting from a primary state of the CFT, we compute the return probability (Pn), equal (Cn) and unequal (Gn) time two-point primary correlators, energy density(En), and the mth Renyi entropy ($$ {S}_n^m $$ S n m ) after n drive cycles. Our results show that below a crossover stroboscopic time scale nc, Pn, En and Gn exhibits universal power law behavior as the transition is approached either from the heating or the non-heating phase; this crossover scale diverges at the transition. We also study the emergent spatial structure of Cn, Gn and En for the continuous protocol and find emergence of spatial divergences of Cn and Gn in both the heating and non-heating phases. We express our results for $$ {S}_n^m $$ S n m and Cn in terms of conformal blocks and provide analytic expressions for these quantities in several limiting cases. Finally we relate our results to those obtained from exact numerics of a driven lattice model.

Fractional Power-Law Intraband Optical Conductivity in the Low-Dimensional Dirac Material CaMnBi2

We studied the broadband optical conductivity of CaMnBi2, a material with two-dimensional Dirac electronic bands, and found that both components of the intraband conductivity follow a universal power law as a function of frequency at low temperatures. This conductivity scaling differs from the Drude(-like) behavior, generally expected for free carriers, but matches the predictions for the intraband response of an electronic system in a quantum critical region. Since no other indications of quantum criticality are reported for CaMnBi2 so far, the cause of the observed unusual scaling remains an open question.

A universal power law for modelling the growth and form of teeth, claws, horns, thorns, beaks, and shells

Background A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes. Results Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants. Conclusions The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.

Supervised learning of few dirty bosons with variable particle number

We investigate the supervised machine learning of few interacting bosons in optical speckle disorder via artificial neural networks. The learning curve shows an approximately universal power-law scaling for different particle numbers and for different interaction strengths. We introduce a network architecture that can be trained and tested on heterogeneous datasets including different particle numbers. This network provides accurate predictions for all system sizes included in the training set and, by design, is suitable to attempt extrapolations to (computationally challenging) larger sizes. Notably, a novel transfer-learning strategy is implemented, whereby the learning of the larger systems is substantially accelerated and made consistently accurate by including in the training set many small-size instances.

AC Conductivity and Conduction Mechanism of Iron (II) Chloride (FeCl2) /Poly (vinyl alcohol) (PVA)/Poly (vinylpyrroldone) (PVP) Polymer Blend Electrolyte

Blend sample based on Poly (vinyl alcohol) (PVA)/Poly (vinylpyrroldone) (PVP), (50:50), and their blend electrolyte with different weigh ratio of Iron (II) Chloride (FeCl2), (0.5, 1 and 2 wt.%), have been prepared using casting method. The AC electrical properties of these samples were investigated in the frequency range 1 kHz to 1 MHz and in temperature ranging from 30 to 150 °C. The real and imaginary impedance, frequency and temperature dependence, indicate the enhancement of the electrical conductivity of the blend due to addition of FeCl2. Pure and electrolyte blend samples were found to be characterized by a plateau region at low frequency and high temperature, and this plateau region increases with increase in temperature and /or FeCl2 weight ratio. Nyquist plots for pure and blend electrolyte samples presented depressed semicircles at all temperatures. For pure blend sample, the ac conductivity was attributed to hopping mechanism while for blend electrolyte sample ionic conduction represents the predominant conduction mechanism. Jonscher universal power law was used to study the conduction mechanism for pure and electrolyte blend sample. The activation energy for blend and blend electrolyte samples was calculated and two activation regions were appeared for blend electrolyte samples.