Value Of Exponent Research Articles

Development of a TGC-based growth model for the olive flounder, Paralichthys olivaceus, and its application in developing a fish growth simulator architecture

Temperature is one of the main factors affecting fish growth. Many studies have proposed a fish growth model considering the effect of temperature. Among these models, the TGC (thermal growth coefficient) model which digitized the influence of temperature on fish growth is the most notable. The original TGC model was made in the form of applying 1/3 as an exponent, but subsequent studies have shown that it is necessary to apply different exponent value or other constant depending on the dynamics of growth. In this study, the original TGC model using 1/3 as an exponent and the new model using 2/3 as an exponent were compared for olive flounder (Paralichthys olivaceus). The seasonal temperature function under the conditions of the flow-through system was applied and the transition point of change in the growth dynamics was obtained by comparing the instantaneous growth rate of the two TGC models. Around 541 g of the transition point was obtained, and a combined TGC model was presented that integrated the two models. However, the growth prediction model based on these statistical techniques does not reflect real-time changes in each parameter and requires academic knowledge, making it difficult to use in the actual field. Recently, as the smart aquaculture industry incorporating ICT (information and communication technologies) has grown rapidly, many solutions such as fish growth prediction simulators using statistical growth models have been developed. Therefore, in this study, input and output variables were classified and software architectures were presented so that the statistical form of fish growth model using TGC derived above could be applied when developing a fish growth prediction simulator. Deriving these growth models and interpreting them into languages in the field of ICT will enhance the field applicability of academic research results as a part of smart aquaculture technology.

Densification mechanism and microstructural evolution of Si3N4 composites with CeO2 as additives during spark plasma sintering

The densification mechanism of CeO2 doped Si3N4 ceramics during spark plasma sintering (SPS) was investigated. The sintering process was observed to undergo significant densification at the intermediate stage of sintering (1435 °C–1816 °C), and the density and grain size of CeO2 doped Si3N4 ceramic were found to be greater than those of pure Si3N4 ceramic under the same sintering conditions. To determine the densification mechanism, a creep model was utilized to determine the densification mechanism which could be interpreted based on the values of the stress exponent (n) and the apparent activation energy (Q d). The results revealed that the Q d of pure Si3N4 (381.15 kJ mol−1) is higher than that of Si3N4-CeO2 powder (265.61 kJ mol−1). Moreover, the stress exponent n of Si3N4-CeO2 powder (1.12–1.33) was higher than that of pure Si3N4 powder (1.00–1.18). This can be attributed to the fact that the addition of CeO2 resulted in the formation of a liquid phase at the grain boundary which leading to a shift in the controlling mechanism from grain boundary diffusion to grain boundary sliding.

Moseley Law for Atomic Orbital Exponents

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Magnetocaloric effect and critical exponents at near room temperature of CrTe

In this work, I investigated and studied the CrTe compound, which has a spin amplitude of about 2, to determine its critical behaviors at near room temperature, magnetocaloric cooling, and magnetic characteristics. For the purpose of this study, I used the Metropolis algorithm with the Monte Carlo approach. The Curie temperature of CrTe is around 326 K, which is determined through the magnetization M(T) and the inverse magnetic susceptibility (χ−1). The Arrott curves (H/M vs. M2) and the isothermal magnetization M(H) demonstrate a second-order ferromagnetic (FM) to paramagnetic (PM) state phase transition. The magnetic entropy change (-ΔSM), relative cooling power (RCP), and refrigeration capacity (Q) at 8 T are 1.31 J kg⁻1 K⁻1, 106 J kg⁻1, and 79 J kg⁻1, respectively. To calculate the critical exponents of CrTe, I used the Widom scaling relation and the modified Arrott plot (MAP). The critical exponent values were found to be in good agreement with those estimated using the renormalization group approach for a 3D-Ising model.

Size-specific variations in the length-weight relationship and relative condition factor of Hilsa shad (Tenualosa ilisha) across its habitats in Bangladesh

The length-weight relationship (LWR) and relative condition factor are widely used as the most important biological parameters to infer the growth pattern and well-being of fishes. The aim of our study was to investigate the growth parameters of the LWR in different growth phases of Hilsa (Tenualosa ilisha), a flagship species of Bangladesh, and compare its relative condition factors across its major habitats. Fish from various rivers in Bangladesh and the Bay of Bengal were sampled, their length-weight growth parameters were measured and subjected to statistical analysis with pooled data from other studies. An isometric growth pattern in Hilsa was predominantly found in the size classes of 25 ≤ TL (total length) < 30, 30 ≤ TL < 35, and TL ≥ 40. However, the size class TL < 25 showed negative allometric growth with the value of the exponent (b, also known as growth coefficient) between 2.797 and 2.833. The highest weight-growth of Hilsa was within the size class of 35 ≤ TL < 40, with exponent values of 3.271–3.381 (positive allometric growth) across habitats. Our results revealed that the exponent value varied significantly (P < 0.05) between different size classes of Hilsa except between 30 ≤ TL < 35 and TL ≥ 40; however, no such significant differences in the exponent values were found across habitats. The Akaike Information Criterion value was lowest for the size-specific length-weight regression model of Hilsa, indicating it was the best-fit model compared to the habitat-specific and pooled sample models. The relative condition factor of Hilsa by habitat was found in the order of Meghna > Bay of Bengal > Andharmanik > Biskhali > Tetulia > Padma. Additionally, the relative physiological well-being of Hilsa from the river Padma and Tetulia was poor compared to that of other habitats. A more in-depth analysis is required to determine the factors that can influence Hilsa's growth and well-being in relation to habitat quality. The present findings have significant relevance for fisheries biologists and managers in understanding and interpreting Hilsa's ecology, relative well-being of populations of same or contrasting habitats, demographic assessment, and for better management of Hilsa in the future.

The breakdown of the direct relation between the density scaling exponent and the intermolecular interaction potential for molecular systems with purely repulsive intermolecular forces

In this work, we question the generally accepted statement that the character of intermolecular interactions can be directly determined from the scaling exponent. We show that the scaling exponent evidently differs on the molecular architecture for pure inverse power law systems. Since these systems are characterized by a well-defined dependency between the intermolecular virial and potential energy, the results contradict theoretical predictions and previous reports. Moreover, we suggest that the recently proposed “molecular force” method also returns the value that varies from the one scaling the dynamics. Finally, the obtained result allows us to conclude that the value of the density scaling exponent for real liquids depends on intramolecular interactions.

Critical behavior of the van der Waals ferromagnet Fe4.8GeTe2

The van der Waals ferromagnet Fe5-xGeTe2 has drawn significant interest due to its approximately room-temperature Curie temperature (TC) of 270 to 310 K, which can be regulated through iron deficiency. To comprehend the tunable TC associated with the ferromagnetic exchange mechanism, we systematically investigate the critical phenomenon of Fe5-xGeTe2 (Fe4.8GeTe2) crystals around TC. Employing diverse analytical methods for magnetization study, we derived reliable critical exponent values: TC = 285 K, β = 0.364(2), γ = 1.293(1), and δ = 4.62(1). Through a comparative analysis of these critical exponents, the magnetic behavior of Fe4.8GeTe2 is expounded as a three-dimensional (3D) magnetic exchange mechanism, with exchange distance decay modeled as J(r) ≈ r−4.85, closely resembling long-range magnetic coupling in the 3D Heisenberg mode.

Hot deformation characteristics and processing map analysis of Al-Zn/stainless steel particles-based composite

The hot deformation behavior of Al-Zn/martensitic stainless steel particles-based composite (Al-Zn/6 %SSp), was examined in this study. The composite was tested using isothermal compression at 200–350 °C/0.01–10 s−1 and a global strain of 0.5. From the results, it was noticed that the composite’s flow stress increased with strain rate increase and drop in temperature. The constitutive equation from the hot-worked composites resulted in an estimated activation energy of 226.27 kJ/mol, which was 58 % more than that for the self-diffusion of aluminum alloy (142 kJ/mol). These findings suggest dynamic recrystallization (DRX) as the dominant deformation mechanism, as confirmed from the microstructures of the hot worked samples mostly at high temperatures and strain rates. Work hardening was predicted to dominate the deformation process by the stress exponent (n) value of 10.36 (which exceeded 5), but this was inconsistent with the microstructural observations. Comparing the linear fitting of calculated flow stress data with the estimated flow stress yielded a correlation coefficient (R2) of approximately 0.97. This observation demonstrates an effective relationship involving the calculated stress with the computed stress value for the composite material that was fabricated. Based on the processing map analysis, the instability regime occurs at 200270 °C/0.01–10 s−1. The stable domain established was at 280–340◦C/0.01–10 s−1 which is most suitable for achieving the best microstructural conditions for enhanced service performance.

Fatigue crack growth study on rolled and cryogenically treated AZ31B Mg alloy plate

This paper investigates the fatigue crack growth rate (FCGR) of AZ31B Mg alloy after cryogenic treatments. Shallow and deep cryogenic treatments were carried out separately at −80οC and −196οC for 12 and 72 hrs, respectively. The microstructural characterization of the cryogenically treated AZ31B specimens was carried out by optical microscope (OM) and X-Ray diffraction (XRD). The small crystalline size structure generated in AZ31B alloy due to the cryogenic treatment further promoted the nucleation of Mg17Al12 phase. Accumulation of dislocation density was also observed in the cryogenically treated specimens. CT specimens were prepared for all three conditions to estimate the FCGR. The as-rolled specimen (R) had higher fatigue resistance than the cryogenically treated specimens. The R specimen’s threshold intensity factor (ΔKth) was higher than the cryogenically treated specimens. The exponent (m) value of the R specimen was lower than the shallow and deep cryogenic treated specimens. Hence, the crack growth resistance was marginally higher in the R specimen compared to the cryogenically treated specimens. However, the critical stress intensity factor (ΔKcr) of cryogenically treated specimens was slightly higher than the R specimen. The post-fracture characterization of the specimens was carried out at three different regions by SEM. The cleavage faces, tear ridges, and voids were noticed in all specimens. The fatigue failure of the R specimen was due to ductile and brittle mode, whereas the cryogenically treated specimen was dominated entirely by brittle fracture.

Out-of-equilibrium scaling of the energy density along the critical relaxational flow after a quench of the temperature.

We study the out-of-equilibrium behavior of statistical systems along critical relaxational flows arising from instantaneous quenches of the temperature T to the critical point T_{c}, starting from equilibrium conditions at time t=0. In the case of soft quenches, i.e., when the initial temperature T is assumed sufficiently close to T_{c} (to keep the system within the critical regime), the critical modes develop an out-of-equilibrium finite-size-scaling (FSS) behavior in terms of the rescaled time variable Θ=t/L^{z}, where t is the time interval after quenching, L is the size of the system, and z is the dynamic exponent associated with the dynamics. However, the realization of this picture is less clear when considering the energy density, whose equilibrium scaling behavior (corresponding to the starting point of the relaxational flow) is generally dominated by a temperature-dependent regular background term or mixing with the identity operator. These issues are investigated by numerical analyses within the three-dimensional lattice N-vector models, for N=3 and 4, which provide examples of critical behaviors with negative values of the specific-heat critical exponent α, implying that also the critical behavior of the specific heat gets hidden by the background term. The results show that, after subtraction of its asymptotic critical value at T_{c}, the energy density develops an asymptotic out-of-equilibrium FSS in terms of Θ as well, whose scaling function appears singular in the small-Θ limit.

Quantum scaling for the metal–insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase’s resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Microstructure, hardness, electrical, and thermal conductivity of SZCN solder reinforced with TiO2 and ZrO2 nanoparticles fabricated by powder metallurgy method

The microstructure and characterization of Sn–Zn–Cu–Ni (SZCN) solder alloy reinforced with TiO2 and ZrO2 nanoparticles (NPs) synthesized by powder metallurgy were investigated. Sn, Zn, Cu and Ni metallic powders were mixed mechanical by 10:1 ball to powder ratio with 300 rpm speed for 2 h. Then 0.5 wt% from nano ZrO2 or TiO2 was mixed by the same parameters with the mixed metal powder. The morphologies and microstructures development during the fabrication process was investigated by X-ray diffractometer (XRD), optical microscope (OM), and scanning electron microscope (SEM) with energy dispersive X-ray spectrometry (EDX). The results reveal an improved distribution of TiO2 or ZrO2 NPs in the SZCN matrix solder, which resulted in an improvement in its density. The analyses of microstructural demonstrated that the addition of TiO2 or ZrO2 NPs to SZCN solder results in the grain refinement of the β-Sn phase, besides the formation of Ni3Sn IMC with small size and uniform distribution. The microhardness was enhanced as a result of the addition of TiO2 or ZrO2 NPs. The experimental results showed that the SZCN-ZrO2 composite solder had the greatest hardness and stress exponent values due to its effectiveness in suppressing the growth of β-Sn grains and the pile-up of dislocations. Both the electrical and thermal conductivities were improved by incorporating TiO2 NPs compared to other solders.

Static recrystallization behavior and strengthening mechanism of a single-phase Cu–18Ni–17Zn alloy

The microstructural evolution and recrystallization behavior of a single-phase Cu–18Ni–17Zn alloy during annealing has been investigated. The strengthening effects of the solute atom concentration, grain size, and recrystallized volume fraction have also been studied. The results have shown that the difference in yield strengths for the fully recrystallized samples mainly depended on the grain boundary strengthening effect. This is attributed to a constant (∼41 MPa) solid-solution strengthening contribution in the completely recrystallized Cu–18Ni–17Zn alloy. When compared with pure copper, this alloy exhibited a high Hall-Petch constant (∼0.36 MPa m1/2), which is due to the higher grain boundary interface energy. A discontinuous recrystallization occurred in the alloy in the temperature range 400 °C–500 °C. Furthermore, the yield strength was linearly correlated to the recrystallized volume fraction in the partial recrystallized samples. Moreover, the addition of Ni and Zn increased the recrystallization temperature and slowed the recrystallization kinetics. The activation energy for the recrystallization was estimated as 92.6 ± 5.1 kJ/mol in the cold-rolled Cu–Ni–Zn alloy, which indicates that the grain boundary migration during recrystallization was mainly controlled by diffusion along the grain boundaries. In addition, the recrystallized grains preferentially nucleated at shear bands with high strain energies in the Cu–Ni–Zn alloy during annealing. As the regions of shear banding were completely consumed, new recrystallized nuclei formed at the grain corners. The limited number of nucleation sites resulted in a low Avrami exponent value that ranged from 0.41 to 0.61.

A modified viscous flow law for natural glacier ice: Scaling from laboratories to ice sheets

Glacier flow modulates sea level and is governed largely by the viscous deformation of ice. Multiple molecular-scale mechanisms facilitate viscous deformation, but it remains unclear how each contributes to glacier-scale deformation. Here, we present a model of ice deformation that bridges laboratory and glacier scales, unifies existing estimates of the viscous parameters, and provides a framework for estimating the parameters from observations and incorporating flow laws derived from laboratory observations into glacier-flow models. Our results yield a map of the dominant deformation mechanisms in the Antarctic Ice Sheet, showing that, contrary to long-standing assumptions, dislocation creep, characterized by a value of the stress exponent [Formula: see text], likely dominates in all fast-flowing areas. This increase from the canonical value of [Formula: see text] dramatically alters the climate conditions under which marine ice sheets may become unstable and drive rapid rates of sea-level rise.

Surface Evolution of Polymer Films Grown by Vapor Deposition: Growth of Local and Global Slopes of Interfaces.

The kinetic roughening of polymer films grown by vapor deposition polymerization was analyzed using the widely accepted classification framework of "generic scaling ansatz" given for the structure factor. Over the past two decades, this method has played a pivotal role in classifying diverse forms of dynamic scaling and understanding the mechanisms driving interface roughening. The roughness exponents of the polymer films were consistently determined as α=1.25±0.09, αloc=0.73±0.02, and αs=0.99±0.06. However, the inability to unambiguously assign these roughness exponent values to a specific scaling subclass prompts the proposal of a practical alternative. This report illustrates how all potential dynamic scaling can be consistently identified and classified based on the relationship between two temporal scaling exponents measured in real space: the average local slope and the global slope of the interface. The intrinsic anomalous roughening class is conclusively assigned to polymer film growth characterized by anomalous "native (background slope-removed) local height fluctuations". Moreover, the new analysis reveals that interfaces exhibiting anomalous scaling, previously classified as intrinsic anomalous roughening, could potentially belong to the super-rough class, particularly when the spectral roughness exponent αs is equal to 1.

Identifying epileptogenic abnormality by decomposing intracranial EEG and MEG power spectra

BackgroundAccurate identification of abnormal electroencephalographic (EEG) activity is pivotal for diagnosing and treating epilepsy. Recent studies indicate that decomposing brain activity into periodic (oscillatory) and aperiodic (trend across all frequencies) components can illuminate the drivers of spectral activity changes. New methodsWe analysed intracranial EEG (iEEG) data from 234 subjects, creating a normative map. This map was compared to a cohort of 63 patients with refractory focal epilepsy under consideration for neurosurgery. The normative map was computed using three approaches: (i) relative complete band power, (ii) relative band power with the aperiodic component removed, and (iii) the aperiodic exponent. Abnormalities were calculated for each approach in the patient cohort. We evaluated the spatial profiles, assessed their ability to localize abnormalities, and replicated the findings using magnetoencephalography (MEG). ResultsNormative maps of relative complete band power and relative periodic band power exhibited similar spatial profiles, while the aperiodic normative map revealed higher exponent values in the temporal lobe. Abnormalities estimated through complete band power effectively distinguished between good and bad outcome patients. Combining periodic and aperiodic abnormalities enhanced performance, like the complete band power approach. Comparison with existing methods and conclusionsSparing cerebral tissue with abnormalities in both periodic and aperiodic activity may result in poor surgical outcomes. Both periodic and aperiodic components do not carry sufficient information in isolation. The relative complete band power solution proved to be the most reliable method for this purpose. Future studies could investigate how cerebral location or pathology influences periodic or aperiodic abnormalities.

Micromechanical and microstructure evolution of leaded (SnPb) and lead-free (SAC305 and SnCu) mixed solder joints during isothermal aging

This paper studies how isothermal aging affects the micromechanical and structural properties of mixed solder joints made of 60Sn-40Pb (SnPb) with Sn-3.0Ag-0.5Cu (SAC305) and SnPb with Sn-0.7Cu (SnCu). The nanoindentation test was done to measure the micromechanical properties of SnPb/SAC305 and SnPb/SnCu mixed solder joints. These properties are hardness, reduced modulus, and stress exponent. Scanning electron microscopy (SEM) was used to look at the microstructure of a cross-section of mixed solder joints. The micrographs that were taken were then examined with open-source image processing software called ImageJ. It was found that the rate and distribution of intermetallic compound (IMC) formation and the reduction of Sn-rich phase grain size affect how the hardness and stress exponent values of mixed solder joints change after 1000 h of high temperature storage (HTS). ImageJ analysis shows that the Pb-rich phase particle count and distribution can be used to figure out how mixed solder joints respond to indentation creep and how that relates to isothermal aging. Using ImageJ, it’s clear that the indentation creep behavior of the GBS mechanism of an as soldered SnPb/SnCu mixed solder joint is caused by the highest number and size of Pb-rich phase particles that are not well distributed across the dendritic area of Sn-rich phase grain boundaries.

Antiepileptic drug-loaded and multifunctional iron oxide@silica@gelatin nanoparticles for acid-triggered drug delivery

The current study developed an innovative design for the production of smart multifunctional core-double shell superparamagnetic nanoparticles (NPs) with a focus on the development of a pH-responsive drug delivery system tailored for the controlled release of Phenytoin, accompanied by real-time monitoring capabilities. In this regard, the ultra-small superparamagnetic iron oxide@silica NPs (IO@Si MNPs) were synthesized and then coated with a layer of gelatin containing Phenytoin as an antiepileptic drug. The precise saturation magnetization value for the resultant NPs was established at 26 emu g-1. The polymeric shell showed a pH-sensitive behavior with the capacity to regulate the release of encapsulated drug under neutral pH conditions, simultaneously, releasing more amount of the drug in a simulated tumorous-epileptic acidic condition. The NPs showed an average size of 41.04 nm, which is in the desired size range facilitating entry through the blood–brain barrier. The values of drug loading and encapsulation efficiency were determined to be 2.01 and 10.05%, respectively. Moreover, kinetic studies revealed a Fickian diffusion process of Phenytoin release, and diffusional exponent values based on the Korsmeyer-Peppas equation were achieved at pH 7.4 and pH 6.3. The synthesized NPs did not show any cytotoxicity. Consequently, this new design offers a faster release of PHT at the site of a tumor in response to a change in pH, which is essential to prevent epileptic attacks.

Experimental research on vibration reduction characteristics of adhesively bonded beam structures with acoustic black hole geometry

Beam structures are widely used in industrial applications such as automobiles, aircraft, naval architecture, trains, and buildings. The vibration characteristics of beams are inherent phenomenon and directly affect usage comfort and service life, but more dangerously may damage the structure due to excessive vibrations that are transmitted through the surrounding structure of the system. Vibration reduction of beam structures is a continuous challenge for industrial applications. It is important to reduce vibrations of the beam structures for stability. In this study, experimental research on vibration reduction characteristics of adhesively bonded beam structures with Acoustic Black Hole technique is presented. The Acoustic Black Hole, which is a geometry, tapered with a power-law profile enables vibration reduction by decreasing the velocity and the wavelength of vibration. The inherent natural vibration properties called modal parameters such as the natural frequencies, damping, and mode shapes of the beam structure with and without damping layer using power-law profile having various the Acoustic Black Hole length and exponent values were investigated and evaluated with experimental modal analysis. For validation, natural frequencies are determined numerically by the finite element method, and then compared with results obtained by the experimental modal analysis. The overall results indicated that the Acoustic Black Hole has ability to significantly suppress the vibration level and showed the capability of enhancing the damping efficiency when using the damping layer attached to the Acoustic Black Hole length of the beam structure.

Sm substitution effect on the critical behaviour of Laves phase Gd1−xSmxCo2 intermetallic nearby the ferromagnetic-paramagnetic phase transition

In this work, we present a comparative and detailed study of the critical behavior near ferromagnetic-paramagnetic phase transition in the intermetallic Laves phase compounds Gd1−xSmxCo2, x = 0.5, 0.6 and 0.7. The investigated samples exhibit a second-order phase transition at Curie temperature TC. The critical exponents β, γ, and δ have been estimated through diverse techniques: the Modified Arrott plot, the Kouvel-Fisher plot, the critical isotherm technique, and the magnetocaloric effect method. The critical exponents values that were determined have been validated using the universal scaling hypothesis, wherein the isotherm magnetization curves M(H) converge into two distinct universal branches below and above TC. The substitution of Gd by Sm changes the universality class in the (Gd,Sm)Co2 compounds. For the sample Gd0.5Sm0.5Co2, the critical exponents obtained are closely consistent with the predictions of the 3D-Heisenberg model featuring a magnetic system with a short-range exchange interaction. While, for both samples Gd0.4Sm0.6Co2 and Gd0.3Sm0.7Co2, the values deviate from known theoretical models and might belong to an unconventional universality class with an intermediate-range exchange interaction.