Scaling Equations Research Articles

Volumetric versus Element-scaling Mass Estimation and Its Application to Permo-Triassic Tetrapods.

Size has an impact on various aspects of an animal's biology, including physiology, biomechanics, and ecology. Accurately and precisely estimating size, in particular body mass, is therefore a core objective of paleobiologists. Two approaches for estimating body mass are common: whole-body volumetric models and individual element-scaling (e.g., bones, teeth). The latter has been argued to be more accurate, while the former more precise. Here, we use minimum convex hulls (MCHs) to generate a predictive volumetric model for estimating body mass across a broad taxonomic and size range (127 g - 2735 kg). We compare our MCH model to stylopodial-scaling, incorporating data from the literature, and find that MCH body mass estimation is both more accurate and more precise than stylopodial estimation. An explanation for the difference between methods is that reptile and mammal stylopod circumference and length dimensions scale differentially (slope 1.179±0.102 vs. 1.038±0.031, respectively), such that reptiles have more robust bones for a given size. Consequently, a mammalian-weighted stylopodial-scaling sample overestimates the body mass of larger reptiles, and this error increases with size. We apply both estimation equations to a sample of 12 Permo-Triassic tetrapods and find that stylopodial-scaling consistently estimates a higher body mass than MCH estimation, due to even more robust bones in extinct species (slope=1.319±0.213). Finally, we take advantage of our MCH models to explore constraints regarding the position of the center of mass (CoM) and find that relative body proportions (i.e., skull:tail ratio) influence CoM position differently in mammals, crocodylians, and Permo-Triassic tetrapods. Further, we find that clade-specific body segment expansion factors do not affect group comparisons but may be important for individual specimens with rather disproportionate bodies (e.g., the small-headed and large-tailed Edaphosaurus). Our findings suggest that the whole-body volumetric approach is better suited for estimating body mass than element-scaling when anatomies are beyond the scope of the sample used to generate the scaling equations and provides added benefits such as the ability to measure inertial properties.

Magnetic phase transition and critical behavior of the chiral magnet [formula omitted]-Mn type Co7Zn7Mn6

We report a systematic study of magnetic transformation and magnetic critical behavior in the chiral magnet β-Mn type Co7Zn7Mn6. It undergoes a paramagnetic-ferromagnetic phase transition around 190 K and shows a spin glass state at 18 K. The critical exponents β= 0.685, γ= 1.385, and δ= 3.03 are obtained by the investigation of magnetic field dependence on magnetic-entropy change and the calculation with Widom scaling relation. The reliability of critical exponents is confirmed by the scaling equation. The strong reversed site disorder of β-Mn type Co7Zn7Mn6 results in the localized characterization of carriers and a slow development of ferromagnetic ordering state.

A variational multiscale stabilized finite element method for double diffusive incompressible flow with application to mixed convection in a heated staggered cavity under magnetic field

In this work, a novel stabilized finite element scheme in a subgrid multiscale variational framework is proposed to efficiently solve double-diffusive incompressible Newtonian fluid flow in a complex geometry occurring in several real-life applications. Here, the fine scale effects are transferred to the course scale problem following algebraic subgrid analysis, and then, the course scale equations are computed and the key stabilization parameters are derived following the Fourier analysis. The influence of flow, heat, and mass transfer parameters such as Reynold’s Number, Hartmann Number, Richardson Number, and Lewis Number are analyzed under a magnetic field, through the streamlines, isotherms, and the local heat fluxes to understand the double-diffusive mixed convective process in a complex staggered cavity, which is relevant to engineering applications such as ventilation and contamination assessment systems. The study finds that maximum species contamination together with the maximum Sherwood Number (12.54) occurs when the Richardson number is 10, and the minimum contamination together with the minimum Sherwood Number (0.71) occurs when the Lewis number is 0.1 when other parameters are varied within the operational range. The results are validated with previously existing literature for simple cases.

Big pythons, big gape, and big prey

Knowing the size of prey that predators can consume facilitates understanding and predicting their ecological impact. Burmese Pythons (Python bivittatus) are apex predators that are larger than all but a few snake species, and their prey, which are swallowed whole, cannot exceed the size of their maximal gape. However, prey sizes smaller than maximal gape may occur because of what snakes select or if capturing and swallowing certain prey is prohibitively difficult. Our study quantified the maximal gape of three large Burmese Pythons (SVLs 410-520 cm), including the longest specimen captured in Florida (where they are invasive) and one specimen that was captured while eating a deer. All three specimens had maximal gape diameters of 26 cm that exceeded the previously reported maximal value of 22 cm, and the soft tissues between the lower jaws accounted for 56-59% of the maximal gape area. Combining our new data with previous data significantly affected the scaling equations predicting maximal gape. The smallest specimen in our study ate a 35 kg deer, which was 93% of its maximal gape area. Hence, in addition to eating prey with large absolute size, Burmese Pythons in nature also eat prey with a size near the limit imposed by gape, but how frequently this occurs remains unclear.

Development of earthquake early warning algorithm magnitude scale for the 2023 Kahramanmaraş earthquake region

On 6 February 2023, Türkiye suffered two major earthquakes with magnitudes of Mw = 7.7 and Mw = 7.6 at 04:17 and 13:24 local time in Pazarcık and Elbistan districts of Kahramanmaraş, which were called as the disaster of the century. On 20 February 2023 at 20:04 local time, another major earthquake with Mw = 6.4 occurred in Yayladağı, Hatay. This disaster caused great loss of life and heavy destruction. The burden of the earthquake on the Turkish economy is extremely heavy. The purpose of earthquake early warning systems (EEWS) is to protect people and property, save time for precautions to be taken and prepare emergency response teams. An effective EEWS has a major role in reducing life, structural and economic losses. This study is an implementation of the original California optimized EPIC, an early warning algorithm, in the region of the 2023 Kahramanmaraş earthquakes. A total of 212 earthquakes in the region are replayed to derive magnitude scaling equations based on peak displacement amplitude (Pd) and predominant period (Tpmax). The performance of the modified equations is tested for three large earthquakes. By comparing the magnitudes estimated by Pd and Tpmax, it is observed that Pd gives more suitable results. The 2023 Kahramanmaras earthquakes real-time tests suggested a warning time of 32 s for the first earthquake in Antakya (Hatay), where the heaviest destruction and loss of life was observed. In the other earthquakes, the warning times were interpreted as quite useful to minimize the loss of life. The geography of the 2023 Kahramanmaraş earthquakes is a seismically active region and will be subject to earthquakes in the future. As a result of this study, a region-specific scaling of the magnitude, which is the most important parameter if an early warning system is established in the region, is presented. It is also a good example of how an effective earthquake early warning system can reduce potential hazards.

A universal yield stress equation for electrorheological fluids

In this study, we investigate the universality of the yield stress [τyE0, where E0 is electric field strength] for examining electrorheological (ER) fluids both experimentally and theoretically. We found that the published experimental data for the yield stress of ER fluids for various materials and measurement conditions obey a yield stress scaling equation. In other words, the ER yield stress data in the literature collapse onto a universal correlation: τ̂=1.313Ê3/2tanhÊ using scaled variables τ̂≡τyE0/τyEc and Ê≡E0/Ec. Here, Ec is critical electric field strength. Although this expression is attractive for experimentalists, this empirical equation has not been derived from first principles. We introduce a mesoscopic elementary region concept and justify this universal correlation for the first time. We decompose the ER system into a finite number of elementary regions and introduce “glueons,” which adhere to neighboring elementary regions resulting in fibrillary structures. We investigated the limiting case when the elementary region size is reduced to zero (continuum limit) and used a reaction-diffusion model to calculate glueon concentration. In modeling the reaction term (generation of glueons), we used a linear model by recognizing that the electric field activates glueons, i.e., the number of glueons increases as the electric field strength increases. In our preliminary study, we were able to justify a universal correlation by solving the glueon concentration equation using a simple geometry. The novelty of this work is the development of universality for the ER yield stress and derivation of a universal scaling equation.

A pore-network modeling perspective on the dynamics of residual trapping in geological carbon storage

This study presents the application of an efficient and robust Dynamic Pore-Network Modeling (DPNM) framework for accurate prediction of carbon dioxide (CO2) trapping behavior under the dynamic flow conditions prevalent in subsurface applications. Residual trapping of CO2 is crucial in the context of geological sequestration, serving as a constitutive relationship that controls relative permeability hysteresis and thereby determining the magnitude of CO2 trapping within formations over varying timescales. Utilizing our DPNM framework, we study the complexities of residual trapping in miniature-core-sized digital replicate of a sandstone. We systematically conduct series of two-phase flow simulations to examine the relationships between total residual CO2 amount, trapping efficiency, and initial saturations across a spectrum of capillary numbers and wettability states. Dynamic simulation results lead to a simple power-law scaling equation correlating CO2 trapping efficiency with initial saturation across various capillary numbers. Further analysis explores the morphological and topological characteristics of fluids during primary drainage and various imbibition displacements within the pore network. This work contributes an essential tool and deepens our understanding of CO2 trapping dynamics, driving progress towards more effective and safer strategies for carbon capture and storage.

Physics-informed scaling laws for theperformance of pitching foils inschooling configurations.

This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations. These relations are derived from quasi-steady lift-based and added mass forces. Hydrodynamic interactions among the schooling foils are considered through vortex-induced velocities imposed on them, constituting the ground effect. Generalized scaling equations are formulated for cycle-averaged coefficients of thrust and power. These equations encompass both the pure-pitching and induced velocity terms, capturing their combined effects. The equations are compared to computational results obtained from two-foil systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 ≤ St ≤ 0.4), pitching amplitude ([Formula: see text]) and phase difference ([Formula: see text]) at Re = 1000-10 000. The individual contributions of pure-pitching and induced velocity terms to propulsive performance elucidate that solely relying on the pure-pitching terms leads to inadequate estimation, emphasizing the significance of the induced velocity terms. The validity of the approach is further assessed by testing it with three-foil and five-foil configurations, which displays a collapse of estimated and measured results. This indicates that the scaling laws are applicable to multi-foil arrangements.

Land of the giants: Body mass estimates of Palaeoloxodon from the Pleistocene of Taiwan

The sea bottom of Taiwan Strait harbors a Late Pleistocene paleo-ecosystem significantly distinct from the present ecosystem structure in Taiwan. The assemblage constitutes fossil remains from the genus Palaeoloxodon, the largest known lineage of proboscideans to have walked on Earth. Body mass holds a pivotal role in our understanding of an organism's biology, ecology, life history, and susceptibility to extinction, and thus, is a key trait while working with extinct taxa. Here we, for the first time, assess the body mass of Palaeoloxodon specimens from Taiwan using well-established allometric scaling equations derived from both extant and extinct species. Our results indicate that Palaeoloxodon individuals from Taiwan exceed 10 tonnes in body mass with a mean body mass of 9.32 tonnes, similar in size to Palaeoloxodon antiquus across Eurasia, and an average shoulder height of 3.49 m. Additionally, our statistical pairwise analysis of body mass distribution shows that Palaeoloxodon specimens from Taiwan significantly differ from the largest species in the genus, Palaeoloxodon namadicus. We further employ equations from extant proboscideans and show notable discrepancies due to differences in body shape between extinct and extant proboscideans. Our estimated body masses offer novel insights into the paleoecology and extinction pressures of the Palaeoloxodon population during the Pleistocene of Taiwan. Further research promises to reveal the habitats capable of sustaining megafaunal populations and extinction events along the easternmost margin of Eurasia.

Critical behaviors of van der Waals itinerant ferromagnet Fe3.8GaTe2

The critical behavior of the van der Waals ferromagnet Fe3.8GaTe2 was systematically studied through measurements of isothermal magnetization, with the magnetic field applied along the c-axis. Fe3.8GaTe2 undergoes a non-continuous paramagnetic to ferromagnetic phase transition at the Curie temperature T c ∼ 355 K. A comprehensive analysis of isotherms around T c utilizing the modified Arrott diagram, the Kouvel–Fisher method, the Widom scaling law, and the critical isotherm analysis yielded the critical exponent of β= 0.411, γ = 1.246, and δ = 3.99. These critical exponents are found to be self-consistent and align well with the scaling equation at high magnetic fields, underscoring the reliability and intrinsic nature of these parameters. However, the low-field data deviates from the scaling relation, exhibiting a vertical trend when T < T c. This discrepancy suggests the occurrence of a first-order phase transition in the crystal under a low magnetic field when T< T c. Mössbauer spectra were employed to provide insights into the critical behaviors of magnetic moments at different sites, including (Fe1)A, (Fe1)B, and Fe2. The results are consistent with the isothermal magnetization analysis. Additionally, the renormalization group theory analysis reveals that the spin coupling within the Fe3.8GaTe2 crystal follows the three-dimensional Heisenberg ({d:n} = {3:3}) type with long-range magnetic and exchange interaction decays with a distance as J(r) ≈ r −4.80.

BASES OF THE METHOD OF PHYSICAL MODELING OF THE PROCESS OF CRUSHING OF MUNICIPAL SOLID WASTE

A large number of studies are aimed at increasing the energy efficiency of grinding processes of various solid materials, while maintaining the values ​​of other important indicators, such as material consumption, productivity, etc. Based on this trend, a new method for physically modeling the process of grinding municipal solid waste (MSW) was proposed for the first time. Existing physical modeling techniques are designed for homogeneous and isotropic materials (for example, soil, crushed stone, snow, coal, etc.). The strength properties of solid waste vary widely due to the significant heterogeneity of their components. Consequently, when crushing solid waste, traditional crusher designs have low efficiency in terms of energy intensity, material intensity and product quality. The purpose of this work is to develop a new technique for physical modeling of the grinding process, based on the main principles of similarity theory and modeling, considering the properties of waste heterogeneity. As a result of the research, a block diagram of the physical modeling methodology for the interaction of the working bodies of impact crushing machines with solid waste was developed. A list of tasks for the modeling process and similarity criteria have been determined based on the development of rheological models of the “working body - municipal solid waste” system and the laws of mechanics that characterize the waste grinding process. Based on the developed similarity criteria, scale equations for the grinding process are substantiated and formulas are derived for determining the expected parameters of the original based on the parameters measured on the model. The developed methodology makes it possible to create a crusher design with improved energy efficiency indicators with the least material and labor costs.

Global population: from Super-Malthus behavior to Doomsday criticality.

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: , and SM-2 is the Malthus-type relation with the time-dependent growth rate or relaxation time τ : . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( to the stretched exponential one ( ). For SM-2 dependence, linear changes of during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior , where is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

Effects of tire wear particles on the water retention of soils with different textures in the full moisture range

Tire wear particles (TWPs) are significant contributors to microplastic pollution in the environment, yet there is limited scientific information concerning their impact on soil hydraulic properties. This study aimed to investigate the impact of TWPs at different concentrations (1, 4, 8, and 16% of the air-dried mass of packed soil samples, w/w) on the water retention curves (WRC) of southern California soils with five different textures (clay, clay loam, silt loam, sandy loam, and loamy sand). The concentrations of 8% and 16% were selected to represent extreme pollution scenarios that might occur near highway corridors. High-resolution water retention data, spanning from saturation to oven dryness, were generated using HYPROP™ and WP4C dew point meter instruments. We also developed WRC scaling equations based on the quantity of TWPs. The bulk density of the samples decreased as the TWP concentration in soils increased. The inclusion of very high concentrations of TWPs (8% and 16% w/w) led to a significant reduction in soil moisture content in the intermediate and dry ranges across various soil textures. However, at the same moisture range, adding 1% TWPs had a minimal impact on soil moisture reduction, while the influence of the 4% TWPs concentration treatment was noticeable only in loamy sand and partially in clay loam soils. Additionally, the overall plant available water decreased with increasing TWP concentrations, except for the clay soil. The texture-specific scaling models exhibited promising performance, with RMSE values ranging from 0.0061 to 0.0120 cm3 cm−3. When bulk density was included as an additional input predictor to construct a single scaling model for all textures, the RMSE increased. Nevertheless, it still indicated a good fit ranging from 0.007 to 0.024 cm3 cm−3, highlighting the suitability of simple scaling for identifying WRC in TWPs-polluted soils, particularly for practical purposes. The findings of this study can contribute to a better understanding and quantification of the impact of TWPs on soil hydrology.

Influence of solvent quality on the swelling and shear modulus of polymer gels chemically cross-linked in solution

The effect of temperature (T) is studied on the swelling of model poly(vinyl acetate) (PVAc) gels in isopropyl alcohol. The theta temperature Θ of these gels, at which the second osmotic virial coefficient A2 vanishes, is close to that of the corresponding high molecular mass polymer solution without cross-links so that solvent quality may be defined in the same way as the corresponding precursor polymer solution. We quantified the swelling and deswelling of PVAc gels relative to their size at the theta temperature, and also determined the effect of T on the shear modulus of these gels. It was found that both swelling and deswelling data could be reduced to a universal scaling equation of the same general form as derived from renormalization group (RG) theory for flexible linear polymer chains in solutions.Graphical abstractVariaton of the volumetric swelling factor as a function of the reduced temperature for PVAc gels swollen in isopropyl alcohol.

Spontaneous imbibition of modified salinity brine into different lithologies: an improvement of comprehensive scaling used for fractured reservoir simulation

Spontaneous water imbibition into matrix blocks can be a significant oil recovery mechanism in fractured reservoirs. Many enhanced oil recovery methods, such as injection of modified salinity brine, are proposed for improving spontaneous imbibition efficacy. Many scaling equations are developed in the literature to predict spontaneous imbibition oil recovery. However, almost none of them included the impact of the diversity in ionic composition of injected and connate brines and the blending/interaction of a low salinity imbibing brine with a higher salinity connate brine. In this research, these two issues are included to propose new scaling equations for the scaling of spontaneous imbibition oil recovery by modified salinity imbibing brines. This study uses experimental data of the spontaneous imbibition of modified salinity brines into oil-saturated rock samples with different lithologies containing an irreducible high salinity connate brine. The collected tests from the literature were performed at high temperatures and on aged altered wettability cores. The results of 110 available spontaneous imbibition laboratory experiments (85, 12 and 13 tests on chalks, dolomites and sandstones, respectively) are gathered. This research initially shows the poor ability of three selected convenient scaling equations from the literature to scale imbibition recovery by modified salinity brine. Then, our newly proposed technique to find the scaling equation for spontaneous imbibition recovery by modified salinity brine, during the abovementioned conditions in limestones (Bassir et al. in J Pet Explor Prod Technol 13(1): 79–99, 2023. https://doi.org/10.1007/s13202-022-01537-7) is used in chalks, dolomites and sandstones to develop the three new scaling equations. Finally, a new general equation to scale imbibition recovery by modified salinity brine for all four lithologies is presented. Moreover, for each of the four datasets (chalk, dolomite, sandstone and all the four lithologies), the scaled data by the new equations is matched by two mathematical expressions based on the Aronofsky et al. model and the Fries and Dreyer model. These mathematical expressions can be used to develop transfer functions in reservoir simulators for a more accurate prediction of oil recovery by spontaneous imbibition of modified salinity brine in fractured reservoirs.

Critical behavior in the ferromagnet

High-Curie-temperature ferromagnets are promising candidates for designing new spintronic devices. Here we have successfully synthesized the single crystal of the itinerant ferromagnet Mn5Ge3 using flux method. Its critical properties were investigated by means of bulk dc magnetization at the boundary of the paramagnetic (PM) and ferromagnetic (FM) phase to determine intrinsic magnetic interactions. Critical exponents with a critical temperature K and with K are acquired by the modified Arrott plot, whereas is deduced by a critical isotherm analysis at K. The self-consistency and reliability of these critical exponents are verified by the Widom scaling law and the scaling equations. Further analysis reveals that the spin interaction in Mn5Ge3 exhibits three-dimensional Ising-like behavior. The magnetic exchange interaction is found to decay as , meaning that the spin interactions exceed the nearest neighbors, which may be related to the different Mn-Mn interactions with inequal exchange strengths.

“Return to equilibrium” anisotropy model for non-equilibrium Reynolds stress closures

A long-standing question in the Reynolds-averaged modeling of turbulent flow is how to predict accurately flows with temporal or spatial unsteadiness. In this paper, we present a “return to equilibrium” approach to modeling the unsteady Reynolds stress anisotropy bij in terms of differential transport equations, the solutions to which are constrained by algebraic closures for bij in flows at equilibrium and by the corresponding rapid-distortion-theory solutions for flows far from equilibrium. When coupled with scale equations for the turbulent kinetic energy and the dissipation rate, these anisotropy evolution equations comprise a complete closure scheme for which no additional model coefficients are required. Evaluations of this closure scheme, in which two different existing equilibrium algebraic models for bij were employed, were carried out for homogeneous turbulence in flows with a step imposition of shear, with continuously oscillatory shear at different frequencies and with a prescribed time-dependent plane-strain rate. Good agreement was achieved between model predictions and experimental/simulation target data in all test cases, with either Girimaji's bij model or a structure-based bij model used as the equilibrium algebraic closure.

Exploring the critical behavior of the anomalous spin-glass transition in Ga1−xMnxS

Single-crystalline Ga1−xMnxS is a quasi-two-dimensional system that exhibits an anomalous spin-glass transition temperature compared with the other well-known spin-glass systems. In contrast to the other known spin-glasses that all have three-dimensional structures, our host chalcogenide GaS system is quasi-two-dimensional. Recent interest in utilizing spin-glass materials for applications in short-term, low-energy memory and processing power make this new 2-D system important for further exploration. We report on the critical behavior of the anomalous spin-glass transition in a single-crystalline Ga0.91Mn0.09S system. Using the scaling equation of state describing the spin-glass transition in Ga1−xMnxS, we obtained the relation χnl = C1H2/δ and extract the value δ = 5.5 ± 0.5 for this critical exponent as well as a value of ϕ = 4.8 for another critical exponent. We find this value of delta for the critical temperature Tc = 11.2 K, combined with the other critical exponents γ = 4.0 and β = 0.8 form a self-consistent description of the spin-glass transition in this unusual 2-D spin-glass system. Interestingly, these results represent convincing evidence that, despite Ga1−xMnxS having a quasi-two-dimensional structure, Ga1−xMnxS undergoes a true spin-glass transition and is related to the class of semiconducting spin-glass materials with short-range interactions. The spin-glass transition in Ga1−xMnxS is characterized by critical exponents similar to the three-dimensional spin-glass systems.

Analysis of scaling relationships for flood parameters and peak discharge estimation in a tropical region

Abstract Relationships between peak discharges and catchment size (e.g., flood scaling) in a catchment have the potential to support new river flood forecasting approaches but have not been tested in tropical regions. This study determined flood scaling relationships between peak discharge and nested drainage areas in the La Sierra catchment (Mexico). A statistical power law equation was applied to selected rainfall–runoff events that occurred between 2012 and 2015. Variations in flood scaling parameters were determined in relation to catchment descriptors and processes for peak downstream discharge estimation. Similar to studies in humid temperate regions, the results reveal the existence of log-linear relationships between the intercept (α) and exponent (θ) parameter values and the log–log power–law relationships between (α) and the peak discharge observed from the smallest headwater catchments. The flood parameter values obtained were then factored into the scaling equation (QP = αAθ) and successfully predicted downstream flood peaks, especially highly recurrent flood events. The findings contribute to a better understanding of the nature of flood wave generation and support the development of new flood forecasting approaches in unregulated catchments suitable for non-stationarity in hydrological processes with climate change.

A ballistic model for subthreshold current and threshold voltage of the dual-material-gate nanosheet MOSFET

— A ballistic model for subthreshold current of the dual-material-gate (DMG) nanosheet (NS) MOSFET is developed based on the Landauer approach, three-dimensional scaling equation, and the continuity of subthreshold current at the interface between the control gate and screen gate in the channel, The work function difference between the screen gate and control gate can be converted into the new interface-quasi-fermi-potential (IQFP) at the junction between different gate regions. Through the IQFP, the ballistic subthreshold current for DMG NS MOSFET is successfully developed. With the determined subthreshold current, the ballistic threshold voltage can also be achieved by the constant current method. Under the low and high drain voltage corresponding to their IQFPs, the subthreshold behavior is mainly governed by the contact potential and thermal voltage, respectively. Furthermore, Ohm's law regarding ballistic resistance for the DMG NS MOSFET can still be valid in the subthreshold conduction.