Single Scaling Research Articles

Critical behavior of the van der Waals bonded ferromagnet Fe3−xGeTe2

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe$_{3-x}$GeTe$_2$ were investigated by bulk dc magnetization around the paramagnetic (PM) to ferromagnetic (FM) phase transition. The Fe$_{3-x}$GeTe$_2$ single crystals grown by self-flux method with Fe deficiency $x \approx 0.36$ exhibit bulk FM ordering below $T_c = 152$ K. The M\"{o}ssbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents $\beta = 0.372(4)$ with a critical temperature $T_c = 151.25(5)$ K and $\gamma = 1.265(15)$ with $T_c = 151.17(12)$ K are obtained by the Kouvel-Fisher method whereas $\delta = 4.50(1)$ is obtained by a critical isotherm analysis at $T_c = 151$ K. These critical exponents obey the Widom scaling relation $\delta = 1+\gamma/\beta$, indicating self-consistency of the obtained values. With these critical exponents the isotherm $M(H)$ curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation $m = f_\pm(h)$, where $m$ and $h$ are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg ($d = 3, n = 3$) spins coupled with the attractive long-range interactions between spins that decay as $J(r)\approx r^{-(3+\sigma)}$ with $\sigma=1.89$.

Critical behaviors of a second order ferromagnetic transition in martensitic state of nominal Ni49Mn39Sb12 alloy

In this study, the critical behaviors around the paramagnetic or the antiferromagnetic to ferromagnetic martensite transition in normal Ni49Mn39Sb12 alloy by bulk magnetization were investigated. The critical exponents (β, γ, and δ) have been obtained by different methods such as modified Arrott plot, Kouvel-Fisher method, and critical isotherm analysis. By these critical exponents, the data of magnetization, field and temperature around TCM collapse into two curves, obeying the single scaling equation M(H,ε)=(ε)βf±[H/ε(γ+β)]. These critical exponents are also confirmed by the Widom scaling law δ=1+γ/β. These exponents are close to those theoretically predicted by mean-field model, indicating that the magnetic interactions are long-range-like ferromagnetism around TC. In addition, the exchange distance has been obtained as J(r)=r−4.52, which also supports the long-range field-mean-like behaviors.

Objective assessment of the reliability of the House-Brackmann and Fisch grading of synkinesis.

The objective of this paper is to assess synkinesis associated with post paretic voluntary facial movements using the objective OSCAR method and to investigate the correlation between synkinesis and paresis to compare the objective results with the subjective scaling systems of Fisch and House-Brackmann. The development of an objective assessment of synkinesis with the OSCAR method is focused on the clinically most relevant eye-mouth and forehead-mouth synkinetic movements. Thirteen patients with unilateral facial paralysis and synkinesis of the University Hospital Zurich were examined. Two types of clinically relevant facial synkinesis were found: a maximal synkinesis and a relative synkinesis. Neither Synkinesis-Index correlates well with the underlying degree of global facial palsy. The relative Synkinesis-Index (rSI) correlates well with the subjective evaluation of synkinesis according to the Fisch Grading, but shows a poor correlation with the traditional House-Brackmann grading. Therefore a single scaling index combining the degree of facial nerve palsy and synkinesis is inappropriate and we propose the use of two independent scaling systems for the evaluation of facial palsy: one for the voluntary facial movements, the other for the involuntary synkinetic movements. The adequate evaluation of the post paretic face should include the results of both scaling systems.

Study of near SOL decay lengths in ASDEX Upgrade under attached and detached divertor conditions

A database with attached, partially detached and completely detached divertors has been constructed in ASDEX Upgrade discharges in both H-mode and L-mode plasmas with Thomson Scattering data suitable for the analysis of the upstream SOL electron profiles. By comparing upstream temperature decay width, with the scaling of the SOL power decay width, based on the downstream IR measurements, it is found that a simple relation based on classical electron conduction can relate and well. The combined dataset can be described by both a single scaling and a separate scaling for H-modes and L-modes. For the single scaling, a strong inverse dependence of, on the separatrix temperature, is found, suggesting the classical parallel Spitzer–Harm conductivity as dominant mechanism controlling the SOL width in both L-mode and H-mode over a large set of plasma parameters. This dependence on explains why, for the same global plasma parameters, in L-mode is approximately twice that in H-mode and under detached conditions, the SOL upstream electron profile broadens when the density reaches a critical value. Comparing the derived scaling from experimental data with power balance, gives the cross-field thermal diffusivity as consistent with earlier studies on Compass-D, JET and Alcator C-Mod. However, the possibility of the separate scalings for different regimes cannot be excluded, which gives results similar to those previously reported for the H-mode, but here the wider SOL width for L-mode plasmas is explained simply by the larger premultiplying coefficient. The relative merits of the two scalings in representing the data and their theoretical implications are discussed.

Syneruptive sequential fragmentation of pyroclasts from fractal modeling of grain size distributions of fall deposits: the Cretaio Tephra eruption (Ischia Island, Italy)

In this work we use fractal statistics in order to decipher the mechanisms acting during explosive volcanic eruptions by studying the grain size distribution (GSD) of natural pyroclastic-fall deposits. The method was applied to lithic-rich proximal deposits from a stratigraphic section of the Cretaio Tephra eruption (Ischia Island, Italy). Analyses were performed separately on bulk material, juvenile, and lithic fraction from each pyroclastic layer. Results highlight that the bulk material is characterized by a single scaling regime whereas two scaling regimes, with contrasting power-law exponents, are observed for the juvenile and the lithic fractions. On the basis of these results, we infer that the bulk material cannot be considered as a good proxy for deducing eruption dynamics because it is the result of mixing of fragments belonging to the lithic and juvenile fraction, both of which underwent different events of fragmentation governed by different mechanisms. In addition, results from fractal analyses of the lithic fraction suggest that it likely experienced a fragmentation event in which the efficiency of fragmentation was larger for the coarser fragments relative to the finer ones. On the contrary, we interpret the different scaling regimes observed for the juvenile fraction to be due to sequential events of fragmentation in the conduit, possibly enhanced by the presence of lithic fragments in the eruptive mixture. In particular, collisional events generated increasing amounts of finer particles modifying the original juvenile GSDs and determining the development of two scaling regimes in which the finer fragments record a higher efficiency of fragmentation relative to the coarser ones. We further suggest that in lithic-rich proximal fall deposits possible indications about the original GSDs of the juvenile fraction might still reside in the coarser particles fraction.

Critical behavior of quasi-two-dimensional semiconducting ferromagnet Cr2Ge2Te6

The critical properties of the single-crystalline semiconducting ferromagnet CrGeTe$_3$ were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents $\beta = 0.200\pm0.003$ with critical temperature $T_c = 62.65\pm0.07$ K and $\gamma = 1.28\pm0.03$ with $T_c = 62.75\pm0.06$ K are obtained by the Kouvel-Fisher method whereas $\delta = 7.96\pm0.01$ is obtained by the critical isotherm analysis at $T_c = 62.7$ K. These critical exponents obey the Widom scaling relation $\delta = 1+\gamma/\beta$, indicating self-consistency of the obtained values. With these critical exponents the isotherm $M(H)$ curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation $m = f_\pm(h)$, where $m$ and $h$ are renormalized magnetization and field, respectively. The determined exponents match well with those calculated from the results of renormalization group approach for a two-dimensional Ising system coupled with long-range interaction between spins decaying as $J(r)\approx r^{-(d+\sigma)}$ with $\sigma=1.52$.

Multiple scaling power in liquid gallium under pressure conditions

Generally, a single scaling exponent, ${D}_{f}$, can characterize the fractal structures of metallic glasses according to the scaling power law. However, when the scaling power law is applied to liquid gallium upon compression, the results show multiple scaling exponents and the values are beyond 3 within the first four coordination spheres in real space, indicating that the power law fails to describe the fractal feature in liquid gallium. The increase in the first coordination number with pressure leads to the fact that first coordination spheres at different pressures are not similar to each other in a geometrical sense. This multiple scaling power behavior is confined within a correlation length of \ensuremath{\xi} \ensuremath{\approx} 14--15 \AA{} at applied pressure according to decay of $G$($r$) in liquid gallium. Beyond this length the liquid gallium system could roughly be viewed as homogeneous, as indicated by the scaling exponent, ${D}_{s}$, which is close to 3 beyond the first four coordination spheres.

Global Phase Diagram of a Three-Dimensional Dirty Topological Superconductor

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random s-wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as Cu_{x}Bi_{2}Se_{3}, is discussed.

Allometry varies among related families of Norway spruce

Key messageSlopes and intercepts of allometric equations for organs’ biomass varied among half-sib families of Norway spruce and between age categories in a family-dependent manner. Genetic variation should be accounted for when applying allometric analysis to mixtures of genetic groups.ContextGenetic variation in relationships among plant biomass components was rarely addressed in trees, though depending on deployment strategies in tree improvement programs, variation among genetic groups in plant organs’ growth rates, and thus biomass allocation, would affect forest growth and carbon balance.AimsWe investigated growth and biomass distribution in Norway spruce (Picea abies [L.] H. Karst) half-sib families. We assumed invariance among families in allometric relationships, and stability in growth rates of different organs between ages 2 and 8 years in the subset of those families. We also tested for ontogenetic trend in allometry using the independent dataset of biomass at age 21 years.MethodsWe analyzed allometric relationships among plant components using standardized major axis regression.ResultsSlopes and intercepts of allometric relationships varied among families, indicating variation in both organs’ growth rates and biomass partitioning at a given plant size. Variation in scaling exponents between age categories was also dependent on the family and plant organ considered.ConclusionVariation in slopes of allometric relationships indicates that a single scaling coefficient should not be applied when different genetic groups are compared. For the interpretation of age effect on biomass partitioning, both slopes and intercepts of allometric relationships should be examined.

Cohesive law describing crack growth at iron/precipitate interfaces

Single dislocations and dislocation pile-ups at crystalline interfaces cause stress concentrations. This can lead to decohesion of the interfaces under tensile loading. To describe this decohesion quantitatively, a cohesive law for planar crack growth at iron/precipitate interfaces is developed. This cohesive law is based on a universal description of the adhesive energy for different interfaces. Only a single scaling factor c must be applied to convert the prediction based on this universal adhesive energy into the actual traction-separation behaviour during crack growth. This scaling factor takes into account the atomic strain and relaxations. The cohesive law derived here can be implemented in a Discrete Dislocation Plasticity framework to describe crack growth at a larger scale. The method presented in this paper for the derivation of a cohesive law can be applied to other material combinations showing brittle crack growth as well.

Comparison of Critical Current Scaling Behaviors in $$\hbox {MgB}_{2}$$ MgB 2 /SiC/Si Thin Films

Scaling behaviors of critical current density $$J_{c}$$ in $$\hbox {MgB}_{2}$$ thin films are investigated on different films with thickness of 100 nm, in comparison with 50- and 10-nm films based on a comprehensive scaling formula. Experimental data are reduced and analyzed with the formula over a wide range of magnitudes. In 100- and 50-nm films the single scaling function has been able to fit experimental $$J_{c}$$ data up to ten orders of magnitudes with appropriate flux pinning parameters. On the other hand, for the 10-nm film, different $$J_{c}$$ dependences were found on temperature and magnetic field, concerning anomalous or granular superconductivity.

Preclinical Pharmacokinetics, Pharmacodynamics, Tissue Distribution, and Interspecies Scaling of Recombinant Human Coagulation Factor XaI16L

FXaI16L is a recombinant human FXa variant which is currently being evaluated in the clinic for treating intracerebral hemorrhage. The aim of our studies is to investigate overall pharmacokinetics, pharmacodynamics, and distribution of FXaI16L in preclinical species, and to understand its potential implication in human. Pharmacokinetics of FXaI16L was examined using active site probes and the results showed that FXaI16L displayed fast clearance, low volume of distribution, and a very short plasma resident time in mice, rats, and monkeys. When pharmacodynamics was examined in monkeys, concentration effects of FXaI16L on shortening of active partial prothrombin time and formation of thrombin-antithrombin complex were observed. Furthermore, biodistribution study was conducted in mice using radiolabeled FXaI16L, and showed that 125I-FXaI16L has high plasma protein binding and significant liver and kidney distribution. Human pharmacokinetic prediction for first-in-human dosing was evaluated using allometric scaling, liver blood flow, and a fixed coefficient method, and single species allometric scaling using monkey data was most predictive for human pharmacokinetics of FXaI16L.

Critical behavior and reversible magnetocaloric effect in multiferroic MnCr2O4

Magnetocaloric effect (MCE) in multiferroic cubic spinel MnCr2O4 (space group Fd3¯m, no. 227, cF56), has been investigated using dc magnetization studies. The values of maximum magnetic entropy change (ΔSMmax) and the adiabatic temperature change (ΔTad) are ∼5.3Jkg−1K−1 and ∼2K, respectively, at ∼42.8K for the magnetic field change of 50kOe. The dc magnetization data near the transition temperature were analyzed by the modified Arrott plots, the Kouvel-Fisher method, log M vs log H, and the scaling analysis. Critical exponents β=0.3932±0.0287, γ=1.0256±0.0239, and δ=3.55±0.26 are obtained around the critical temperature ∼42.88K. The critical exponents are in excellent agreement with the single scaling equation of state M(H,∊)=∊0.3932±0.0287f±(H/∊((0.3932±0.0287)+(1.0256±0.0239))); with f+ for T>42.88K, f- for T<42.88K, and ∊=(T−42.88)/42.88. At T=42.88K, the exponent δ relates the magnetization with applied filed by M=H1/(3.55±0.26). Scaling analysis shows that calculated critical exponents as well as critical temperature are intrinsic to the system. Theoretically, the value of β is close to 3D Heisenberg model, while values of γ and δ are close to those of the mean field model. So the values of critical exponents indicate that the critical behavior of MnCr2O4 cannot be described within the framework of existing universality classes and probably belong to a separate class.

Critical behavior near the ferromagnetic to paramagnetic phase transition temperature in polycrystalline La0.5Sm0.1Sr0.4Mn1−xInxO3 (0 ≤ x ≤ 0.1)

In this paper we report on the critical analysis of the La0.5Sm0.1Sr0.4Mn1−xInxO3(0⩽x⩽0.1) manganites near the ferromagnetic-paramagnatic phase transition temperature. Various techniques such as modified Arrott plot, Kouvel–Fisher method and critical isotherm were used to analyze the magnetic-field dependence of magnetization. The Curie temperature (TC) could be tuned over a wide temperature range, from 251K to 310K, with varying in content. Though the nature of this transition is found to be of second order, the estimated critical exponents β, γ, and δ obtained for different values of x are close to the theoretically predicted values for the three-dimensional (3D)-Ising interaction model (β=0.324±0.01, γ=1.240±0.13 at TC=310K for x=0.00); (β=0.329±0.04, γ=1.241±0.001 at TC=294K for x=0.05); (β=0.332±0.01, γ=1.250±0.04 at TC=251K for x=0.10) and are very far away from any other known universality class. The critical isotherm M (TC, µ0H) gives δ=5.02±0.01 for x=0.00. Thus, the scaling law δ=1+γ/β is fulfilled. The critical exponents obey the single scaling equation of M(μ0H,ε)=εβf±(μ0H/εβ+γ); where f+ for T>TC and f− for T<TC.

Physics of chewing in terrestrial mammals

Previous studies on chewing frequency across animal species have focused on finding a single universal scaling law. Controversy between the different models has been aroused without elucidating the variations in chewing frequency. In the present study we show that vigorous chewing is limited by the maximum force of muscle, so that the upper chewing frequency scales as the −1/3 power of body mass for large animals and as a constant frequency for small animals. On the other hand, gentle chewing to mix food uniformly without excess of saliva describes the lower limit of chewing frequency, scaling approximately as the −1/6 power of body mass. These physical constraints frame the −1/4 power law classically inferred from allometry of animal metabolic rates. All of our experimental data stay within these physical boundaries over six orders of magnitude of body mass regardless of food types.

R Peak Detection Algorithm based on Continuous Wavelet Transform and Shannon Energy

The R peak detection algorithm is a necessary tool for monitoring and diagnosing the cardiovascular disease. This paper presents the R peak detection algorithm based on continuous wavelet transform (CWT) and Shannon energy. We evaluate the proposed algorithm with the 48 record of ECG data from MIT-BIH arrhythmia database. Results show that the proposed algorithm gives very good DER (0.48%-0.50%) compared to those from previous publications (0.168%-0.87%). We demonstrated that the use of the CWT with a single scaling parameter is capable of removing noises. In addition, we found that Shannon energy cannot improve the DER value but it can highlight the R peak from the low QRS complex in ECG beat leading to the improvement in the robustness of the R peak detection algorithm.

Excitonic absorption spectra in graphene nanoflakes: Tuning of exciton binding energy by dielectric environments.

By solving the Bethe-Salpeter equation within the Hartree-Fock formalism, we study the excitonic absorption spectra of graphene nanoflakes embedded in various dielectric environments. With the excitonic effects fully taken into account, the exciton binding energy as a function of the dielectric constant is found to be well described by a single scaling rule in which the scaling factor is found to vary slowly with the size of the nanoflakes. Furthermore, it is revealed that the exciton binding energy scales almost linearly with the on-site interaction energy and exhibits more sensitive dependence in smaller nanoflakes. Our results are found to agree well with the recent experiment.

Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

We show that exact time dependent single particle Green function in the Imambekov–Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlevé IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy–Widom result connecting the Airy kernel with Painlevé II. The asymptotic power law of the exact solution as a function of a single scaling variable x/\sqrt{t}x/t agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

Generalized Knudsen Number for Unsteady Fluid Flow.

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance.

Multifractal characteristics of magnetospheric dynamics and their relationship with sunspot cycle

Multifractal analysis deals with a process whose power-law scaling behavior is a nonlinear function of statistical moments having a spectrum of scaling exponents. In contrast, monofractal process has a scaling behavior which is a linear function of moments with a single scaling exponent. In this study, multifractal analysis of complex magnetosphere using box-counting approach has been considered for a better understanding of intermittent and persistent features, focusing on the auroral electrojet index (AE), SYM-H and Dst indices. For the analysis, 1-min AE, SYM-H and Dst indices are taken during the interval 1985–2007. We compare the sunspot cycle dependence of self-similarity and multifractality of magnetospheric proxies such as AE, SYM-H and Dst indices, using both monofractal and multifractal paradigms. The results indicate that monofractal features of AE, SYM-H and Dst indices are solar activity dependent. But, while analyzing the multifractal features, multifractal spectrum of AE index is less dependent on solar activity when compared with that of SYM-H and Dst indices. This implies that, other than solar wind forcing, certain complex phenomena of internal origin also modify the dynamics of geomagnetic fluctuations in the high-latitude auroral region.