Change Of Exponents Research Articles

Lyapunov exponents and phase transitions of Born-Infeld AdS black holes

In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for timelike geodesics in background metric and photon geodesics in effective metric. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent 1/2 near critical point.

Linear Version of the Anti-Perron Effect of Change of Positive Characteristic Exponents to Negative Ones

Linear Version of the Anti-Perron Effect of Change of Positive Characteristic Exponents to Negative Ones

Effect of drop‐size parameterization and rain amount on blade‐lifetime calculations considering leading‐edge erosion

AbstractLeading‐edge erosion (LEE) of wind turbine blades is caused by the impact of particles, for example, raindrops, and leads to a loss in the power production and high maintenance cost. Investigations have shown that a reduction in tip speed, so‐called erosion‐safe mode, increases the blade lifetime but the influence of different drop‐size parameterizations and rain amounts on the blade lifetime is unclear. This study compares blade lifetime calculations using two different drop‐size parameterizations, which both describe a characteristic drop size of a rain measurement. Furthermore, changes in blade lifetime in case rain amount is increased or decreased are investigated as well as the effect of different wind shear exponents. The blade‐lifetime calculations are based on a kinetic‐energy model and an accumulated rain model. The results show that a drop‐size parameterization based on rain rate leads to 44 times longer blade lifetime compared with a parameterization using in situ drop‐size measurements. This large difference is probably due to the underestimation of large drops of the first mentioned parameterization. A change in rain amount of about ±17 % results only in a marginal change in blade lifetime. For both cases and models, an extension of blade lifetime was calculated when reducing the tip speed during specific rain events. The change of wind shear exponents caused as well a considerable effect on the lifetime prediction. Overall, blade lifetime is primary depending on the chosen model, where the kinetic‐energy model is highly sensitive to the drop‐size parameterization.

Bose system critical dynamics near quantum phase transition

We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose–Einstein employing the Keldysh–Schwinger approach and develop the renormalization group technique that enables us to obtain analytical expressions for temperature dependencies of critical exponents.

Conditional symmetry: bond for attractor growing

Coexisting attractors with conditional symmetry exist in separated asymmetric basins of attraction with identical Lyapunov exponents. It is found that when a periodic function is introduced into the offset-boostable variable, infinitely many coexisting attractors may be coined. More interestingly, such coexisting attractors may be hinged together and then grow in the phase space as the time evolves without any change of the Lyapunov exponents. It is shown that, in such cases, an initial condition can be applied for selecting the starting position; consequently, the system will present a special regime of homogenous multistability. Circuit implementation based on STM32 verifies the numerical simulations and theoretical analysis.

Gaussian free field in the iso-height random islands tuned by percolation model

The Gaussian free field (GFF) is considered in the background of random iso-height islands which is modeled by the site percolation with the occupation probability p. To realize GFF, we consider the Poisson equation in the presence of normal distributed white-noise charges, as the stationary state of the Edwards–Wilkinson model. The iso-potential sites (metallic sites in the terminology of the electrostatic problem) are chosen over the lattice with the probability 1 − p in the percolation model, giving rise to some metallic islands and some active (not metallic, nor surrounded by a metallic island) area. We see that the dilution of the system by considering these metallic regions annihilates the spatial correlations and also the potential fluctuations. Some local and global critical exponents of the problem are reported in this work. The GFF, when simulated on the active area show a cross over between two regimes: small (UV) and large (IR) scales. Importantly, by analyzing the change of exponents (in and out of the critical occupation pc) under changing the system size and the change of the cross-over points, we find two fixed points and propose that is unstable towards GFFp=1.

Effect of sintering temperature on structural, magnetic, magnetocaloric and critical behaviors of Ni-Cd-Zn ferrites prepared using sol-gel method

We have investigated the effect of sintering temperature on structural, magnetic, magnetocaloric and critical behaviors of Ni0.4Cd0.3Zn0.3Fe2O4 ferrites synthesized using sol-gel method at 900 °C and 1100 °C. X-ray diffraction patterns indicated that samples crystallize in the cubic spinel structure (Fd3‾m space group) with an increase of lattice constant and average crystallite size as the sintering temperature increases. Magnetic measurements revealed that that the prepared samples undergo second-order ferromagnetic (FM) to paramagnetic (PM) phase transitions. An increment in magnetization, Curie temperature, magnetic entropy change and relative cooling power has been observed with increasing the sintering temperature. The magnetic entropy change reached maximum values of about 1.11 J.kg−1.K−1 and 1.62 J.kg−1.K−1 for μ0H = 5 T corresponding to relative cooling power (RCP) of 152.09 J.kg−1 and 253.65 J.kg−1 for samples sintered at 900 °C and 1100 °C, respectively. These values are comparable favorably with those of some others ferrites considered as possible candidates for magnetic refrigeration. The estimated critical exponents obtained for sample sintered at 1100 °C are close to the tricritical mean-field model; whereas for sample sintered at 900 °C, the exponents belong to a different universality class. This change of critical exponents is mainly due to the increase of average crystallite size as the sintering temperature increases.

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

We study the critical order parameter fluctuations of the absorbing-state phase-transition exhibited by branching and annihilating random walkers performing anomalous diffusion in a linear chain. The diffusion process is considered to follow a power-law distribution of jump lengths with a typical decay exponent α. We focus in the case of parity conserving dynamics for which deviations from the usual directed percolation universality class have been previously demonstrated even for the limiting cases of normal diffusion. Anomalous diffusion induces a continuous change of the critical exponents. By performing a finite-size scaling analysis of simulation data, we show that the critical order parameter moment ratio also varies continuously with α. We unveil that the critical order parameter distribution evolves from a nearly Gaussian to an exponential form as the range of the jump distribution is increased up to the limit on which the active state predominates for any finite branching probability.

Application of gravity model on the Korean urban bus network

Abstract Mobility models have been studied to describe the underlying mechanism of human mobility. The mobility patterns in various transportation systems were understood with the gravity model by estimating the traffic as a simple function of population and distance. Compared to most studies on large-scale systems, we focused on the validity and characteristics of gravity model for intraurban mobility. Several variations of gravity model are applied on the urban bus systems of five medium-sized cities in Korea. The gravity model successfully estimates the intraurban traffic without universal exponents for cities. From the change of exponents by predictor types, we figure out the effect by a non-trivial relation between traffic and population in the urban areas.

Effects of age classes on metabolic exponents of Salix psammophila branches.

Metabolisms are fundamental processes of organisms. They are related to carbon and water cycling of a plant. The relationship between the metabolic rate and the body size of an organism has been a hot spot in ecological research. The typical WBE model with 3/4 power has been controversial. This study tested the applicability of WBE model and examined the change of metabolic exponents with the age class at branch scale in a typical plant, Salix psammophila in the southern edge of the Mu Us desert. The results showed that the estimated metabolic exponent based on the leaf biomass and total biomass was 0.97 for all branches of the S. psammophila. This was significantly greater than the constant power of 3/4 proposed by the WBE model. The branching radius exponent and branching length exponent were 2.67 and 3.83, respectively, being significantly greater than the constant values of 2.0 and 3.0, respectively. The ranges of branching radius exponents and branching length exponents among the age classes were 2.64-3.24 and 2.86-4.30, respectively. Meanwhile, the estimated values and calculated values of metabolic exponents ranged from 1.01-1.29 and 0.94-1.13, respectively. The values of all above were statistically indistinguishable among the six age classes. The common slopes among the six age classes for estimated values and calculated values of metabolic exponents, branching radius exponents and branching length exponents were 1.08, 1.00, 2.84 and 3.35, respectively. These values were significantly greater than the constant values. The changes of the intercept at the y-axis shifted negatively at the common slope of estimated metabolic exponents with significant elevation shift between groups, and the higher age class branches had the greater shift. These indicated that the age classes did not change the metabolic exponents, but changed the metabolic constant significantly. The older branches had lower metabolic activity than the younger branches.

Discussion of “Rapid Prediction of Hydraulic Performance for Emitters with Labyrinth Channels” by Jun Zhang, Wanhua Zhao, and Bingheng Lu

The authors are appreciated for presenting a rapid prediction method of hydraulic performance evaluation for emitters with labyrinth channels. In that procedure, a variable pressure loss coefficient (PLC) was proposed as the evaluation index of an emitter’s hydraulic performance. As a matter of fact, the authors’ previous work (Zhang et al. 2011b) was focused on the same concern with testing the hydraulic performance of specific types of emitters with labyrinth channels. In that procedure (Zhang et al. 2011b), the combined pressure loss coefficient (PLC) was also proposed as an evaluation index which incorporates the effects of frictional and local losses in labyrinth channels. Regarding the same concern, Zhang et al. (2011a) proposed an alternative procedure for testing hydraulic performance of three of the most commonly available high-head in-line drip-tape emitters under different working-head conditions ranging from 0.2 to 10 m, especially for low-head conditions. This analysis (Zhang et al. 2011a) mainly deals with the calculation of the coefficient of manufacturing variation (CV ) and the emitter flow exponent (x), regarding different phases of water pressures. For the design problem of testing emitter hydraulic performance, these three successively published procedures (Zhang et al. 2011a, b, and the paper under discussion) may provide a useful decision support tool for achieving a good design solution among commercially available alternatives with high water application uniformity, and the resulting high irrigation efficiency. With respect to the current problem (testing the emitter hydraulic performance), Qingsong et al. (2010) presented an experimental procedure to simulate the change of emitter flow exponents with different ranges of water pressures examined. The analysis (Qingsong et al. 2010) mainly deals with, first, the calculation of the emitter flow exponent, the average flow velocity, and the Reynold numbers with regarding different phases of water pressures, and then the determination of the best choice among the pressure ranges examined for five types of drip emitters tested. For these purposes, the paper is essentially focused on three research topics: (1) the change of flow exponents with different pressure segments; (2) the relationship between average flow velocities and water pressures, and (3) the relationship between Reynolds numbers and flow exponents. As a useful reference, Yildirim (2010) proposed the backward stepwise procedure for computing three energy loss components; minor friction losses through the path of an integrated in-line emitter, the local pressure losses due to barbed emitter connections, and the pipe friction loss. In that procedure, the mathematical expressions were implemented in a simple Excel spreadsheet to evaluate the relative contribution of each energy loss component; then a combination calculation procedure is used to calculate total energy loss. Two sample designs were evaluated in order to show the relative magnitudes of total friction loss (due to pipe and emitters) emitter local losses, and pipe friction loss for two kinds of the integrated in-line emitters with varying spacing. In order to better understand the present method this discussion calls attention first to the following standpoints which need to be clarified, and then to minor editorial corrections on the paper’s algorithm, which will be presented through the discussion.

Closure to “Experimental Study on the Multisegment Regime of the Water Flow in Drip Emitters” by Wei Qingsong, Lu Gang, Wang Li, Zheng Jincan, Liu Jie, and Shi Yusheng

The authors are appreciated for presenting an experimental procedure that simulates the change of emitter flow exponents with different ranges of water pressures examined. The present analysis first deals with the calculation of the emitter flow exponent, the average flow velocity, and the Reynolds numbers with regard to different phases of water pressures, then with the determination of the best choice among the pressure ranges examined for five types of drip emitters tested. For these purposes, this paper is essentially focused on three research topics: (1) change of flow exponents with different pressure segments, illustrated by the original paper’s Table 4 and Figs. 1 and 2; (2) the relationship between average flow velocities and water pressures, illustrated by the original paper’s Figs. 3 and 4; and (3) the relationship between Reynolds numbers and flow exponents, illustrated by the original paper’s Figs. 5 and 6. Although the statistical results from the present experimental research in the original paper’s “Conclusions” section are found to be satisfactory, the discusser calls attention to the following points that still require further clarification. To avoid any notation conflict, the notations or definitions are the same as those in the original paper. The paper presents Eq. (3) for the relation between the average flow velocity (v) and emitter discharge (q) in the following form: v 1⁄4 q 3.6 × 10As First, to clearly understand Eq. (3), one must know what the average flow velocity (v) means (average flow velocity inside the emitter or average flow velocity in the pipe). From the reasonable definition that it is the average flow velocity inside the emitter, it is required to derive a mathematical expression between the average flow velocity inside the emitter and the Reynolds number for the emitter flow, depending on both the pipe and the emitter geometric characteristics. Yildirim (2010) offered a simple mathematical model based on the stepwise procedure to accurately determine the pressure head profile along the lateral line. Essentially, this work extends to the previous discussion (Yildirim 2006a) on the original research of Provenzano and Pumo (2004) for a systematic comparison of different kinds of in-line/on-line emitters and various design configurations. In that paper, relative contributions of each of the energy loss components are calculated with the appropriate mathematical equation. Integrated in-line emitters cause contraction of the flow path at the upstream connection between the emitter and the lateral pipe and the expansion of the flow path immediately downstream from the emitter; thus, an additional minor friction loss must be considered (Provenzano and Pumo 2004). Integrated in-line emitters have an inner diameter, Dg (m), that is smaller than the pipe’s inner diameter,Di (m); therefore, the emitters determine higher frictional head losses because of the lower cross-section area. Emitter friction loss per unit emitter length, Je (m=m), can also be evaluated by the Darcy-Weisbach formula (Yildirim 2010):

Multidimensional analog of the two-dimensional perron effect of sign change of characteristic exponents for infinitely differentiable differential systems

We obtain a general n-dimensional analog of the two-dimensional (partial) Perron effect of sign change of all arbitrarily prescribed negative characteristic exponents of an n-dimensional differential system of the linear approximation with infinitely differentiable bounded coefficients to the positive sign for the characteristic exponents of all nontrivial solutions of a nonlinear n-dimensional differential system with infinitely differentiable perturbations of arbitrary order m > 1 of smallness in a neighborhood of the origin and growth outside it. These positive exponents take n values distributed over n arbitrarily prescribed disjoint intervals and are realized on solutions issuing from nested subspaces R1 ⊂ R2 ⊂ ... ⊂ Rn.

Experimental Study on the Multisegment Regime of the Water Flow in Drip Emitters

The flow exponent greatly determines the hydraulic performance of drip emitters. The objective of this study is to reveal the change of flow exponents with different water pressures. Laboratorial experiments of the relationship between discharges and water pressures were conducted with five types of drip emitters used for surface drip irrigation systems. The regression for calculating flow exponents was done with different segment pressures. The results showed that the flow exponent reduced gradually with the increase of the pressure segment except a brief increase in the early stage of pressure increasing due to the channel expansion. The eddy drip-arrow is most suitable for the pressure ranges of 2–8 and 8–14 mH2 O . The effect of the use of the small diameter drip-tube is best in the high-pressure range of 17–25 mH2 O . The relation between average flow velocities and water pressures is characterized by the flow exponent, the same as that between emitter discharges and water pressures. The eddy drip-...

Detection of ship targets on the sea surface based on Lyapunov exponents of image block

The change of background's chaos feature when there are moving targets was analysed, and a new algorithm based on Lyapunov exponents of image block for moving targets detection on the sea surface, which is used for ship targets detection on the sea surface, was proposed. The new method defines the term of image gray level distance, extends the calculation method of Lyapunov exponents from single dimension signal to image signal based on the improved Wolf method, uses the change of the largest gray level distance Lyapunov exponents to detect ship targetssubmerged in chaos background. Experimental results show that the sea surface background has chaos feature. The proposed algorithm can detect ship targets effectively and can get better result than statistical analysis.

Phase synchronization of coupling systems

The influence of the linear and nonlinear coupling parameters on the phase synchronization of chaos between two sub-systems with primary resonance is investigated by introducing the conception of the phase for a chaotic motion. The evolution process from non-synchronized state to imperfect phase synchronization and further to perfect phase synchronization between two sub-systems with approximate primary resonance is discussed. Further investigation reveals that the transition between different phase states are related to the critical change of the Lyapunov exponents. The results show that phase synchronization between two sub-systems is enhanced with the increase of the linear coupling strength and decayed with the increase of nonlinear coupling strength.

Drift causes anomalous exponents in growth processes.

The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This mechanism represents a relevant perturbation and therefore is important for the interpretation of experimental and numerical results. In effect, the mechanism leads to the roughness exponent assuming the same value as the growth exponent. In the case of the Edwards-Wilkinson equation this implies exponents deviating from those expected by dimensional analysis.

Effect of nonlinearity of the middle term of nonlinear dispersive equations on physical structures

In this work we study the effect of nonlinearity of the middle term of a class of nonlinear dispersive equations on the physical solutions. We show that the change of the exponent of the middle term plays a major role in exhibiting compactons, solitons and periodic solutions. Three model equations are adopted to carry out this study. The analysis reveals a change of the physical solutions as a result of the change of exponents.

Statistical analysis of rockfall volume distributions: Implications for rockfall dynamics

We analyze the volume distribution of natural rockfalls on different geological settings (i.e., calcareous cliffs in the French Alps, Grenoble area, and granite Yosemite cliffs, California Sierra) and different volume ranges (i.e., regional and worldwide catalogs). Contrary to previous studies that included several types of landslides, we restrict our analysis to rockfall sources which originated on subvertical cliffs. For the three data sets, we find that the rockfall volumes follow a power law distribution with a similar exponent value, within error bars. This power law distribution was also proposed for rockfall volumes that occurred along road cuts. All these results argue for a recurrent power law distribution of rockfall volumes on subvertical cliffs, for a large range of rockfall sizes (102–1010 m3), regardless of the geological settings and of the preexisting geometry of fracture patterns that are drastically different on the three studied areas. The power law distribution for rockfall volumes could emerge from two types of processes. First, the observed power law distribution of rockfall volumes is similar to the one reported for both fragmentation experiments and fragmentation models. This argues for the geometry of rock mass fragment sizes to possibly control the rockfall volumes. This way neither cascade nor avalanche processes would influence the rockfall volume distribution. Second, without any requirement of scale‐invariant quenched heterogeneity patterns, the rock mass dynamics can arise from avalanche processes driven by fluctuations of the rock mass properties, e.g., cohesion or friction angle. This model may also explain the power law distribution reported for landslides involving unconsolidated materials. We find that the exponent values of rockfall volume on subvertical cliffs, 0.5 ± 0.2, is significantly smaller than the 1.2 ± 0.3 value reported for mixed landslide types. This change of exponents can be driven by the material strength, which controls the in situ topographic slope values, as simulated in numerical models of landslides [Densmore et al., 1998; Champel et al., 2002].

A scaling analysis of ER‐2 data in the inner Arctic vortex during January–March 2000

We apply multifractal analysis using exponents H1, C1, and α to straight and level stratospheric flight legs of the ER‐2 high‐altitude research aircraft in the inner vortex (defined as having wind speed <30 ms−1). The quantities so analyzed were ozone, wind speed s and temperature T, with the more gappy NOy data being analyzed by H1 alone. The results for ozone, wind, and temperature are presented as time‐dependent data on the three possible planes of the exponents and are compared for the different variables. We relate values of H1 found in January observations of NOy to those found for ozone. Inner vortex mixing does not remove the small‐scale polar stratospheric cloud‐induced antipersistence (negative correlation between neighboring intervals for all choices of interval) in ozone by mid‐March. Given that large particles were in evidence on all flights examined up to and including 7 March (although in greatly decreased numbers compared to January), this is reasonable. The value of α for ozone did, however, show an increase by mid‐March, consistent with the widespread ozone loss evident from time series of histograms of ozone and methane. The histograms also demonstrate that inhomogeneity, with long tails in the probability distributions, is maintained throughout at the 15–25% level in both species. Interpretation is made in terms of polar stratospheric cloud (PSC) induced antipersistence competing with persistence induced by the large‐scale insolation field, with the balance increasingly favoring the latter as time proceeds. Results are compared with inner vortex data obtained during earlier ER‐2 flights in the Antarctic (1987) and in the Arctic (1989). The inner vortex over Antarctica showed significant increases in H1(O3) and α during mid to late September. The correlated increases are consistent with latitudinal excursions of the outer vortex after the cessation of PSC processing, with increased solar exposure increasing H1(O3) and a greater variety of filaments increasing α(O3). It is concluded that the results have implications for the calculation of photochemical ozone loss in the vortex as a function of time and show that the combined effects of Bolgiano‐Obukhov k−11/5 vertical scaling and Kolmogorov k−5/3 horizontal scaling predict the scaling behavior of wind speed observed by the aircraft. Rates of change of scaling exponents are linked to horizontal mixing rates and are combined with rates of change of methane to estimate diabatic descent and ozone loss rates for the inner vortex.