First-order Effects Research Articles

Trade and economic growth: Does the sophistication of traded goods matter?

Since the appearance of the seminal paper of Frankel and Romer (Am Econ Rev 89(3): 379–399, 1999), ‘Does trade cause growth?’, the impact of aggregate trade openness on income has been controversial. This research shows that the type of product that is traded has first-order effects, while overall trade intensity has second-order effects on per capita income because of (i) the hierarchical structure of learning-by-doing in products with different levels of sophistication of the production processes; and (ii) the fertility and education effects of trade specialization following the quantity–quality tradeoff framework of Galor and Mountford (Am Econ Rev 96(2): 299–303, 2006). Using data on trade disaggregated by the level of technological sophistication of the production process for 223 countries over the period 1962–2019, we find that (1) the effects of foreign trade on income differ widely across technology categories; (2) high-tech trade has permanent growth effects; and (3) a significant fraction of the impact of trade on income is mediated through education and fertility.

Beyond steric selectivity of ions using ångström-scale capillaries.

Ion-selective channels play a key role in physiological processes and are used in many technologies. Although biological channels can efficiently separate same-charge ions with similar hydration shells, it remains a challenge to mimic such exquisite selectivity using artificial solid-state channels. Although there are several nanoporous membranes that show high selectivity with respect to certain ions, the underlying mechanisms are based on the hydrated ion size and/or charge. There is a need to rationalize the design of artificial channels to make them capable of selecting between similar-sized same-charge ions, which, in turn, requires an understanding of why and how such selectivity can occur. Here we study ångström-scale artificial channels made by van der Waals assembly, which are comparable in size with typical ions and carry little residual charge on the channel walls. This allows us to exclude the first-order effects of steric- and Coulomb-based exclusion. We show that the studied two-dimensional ångström-scale capillaries can distinguish between same-charge ions with similar hydrated diameters. The selectivity is attributed to different positions occupied by ions within the layered structure of nanoconfined water, which depend on the ion-core size and differ for anions and cations. The revealed mechanism points at the possibilities of ion separation beyond simple steric sieving.

Augmentation of the stable static travel range of electrostatically actuated slender nano-cantilevers by accounting for the influence of the van der Waals force

The van der Waals (vdW) force, along with the electrostatic force and the first-order fringing field effect, act on the electrostatically actuated nano-cantilever (EANC) when the gap between the deformable electrode and the stationary electrode is less than 20 nanometres. Because of the vdW force, the EANC can undergo a pull-in phenomenon even without the electrostatic force when the nano-cantilever length exceeds its detachment length. The vdW force also results in a significant reduction in static pull-in instability parameters of the slender EANC compared to corresponding parameters obtained when this force is absent. This paper aims to augment the stable static travel range (i.e., the pull-in displacement) of the aforementioned EANC having a length close to its detachment length by varying the beam width. The beam width is assumed to vary in linear and parabolic manners and is controlled using a width variation parameter in each case. The governing equation of the Bernoulli-Euler beam theory and the Galerkin’s technique are utilised to obtain the weighted residual statement (GWRS). The GWRS is utilised to obtain static pull-in instability parameters of referential prismatic and variable-width EANCs. Pull-in instability parameters of variable-width EANCs, for various values of width variation parameters and the initial gap between electrodes, have been obtained. The aforementioned results have been validated with corresponding results obtained by three-dimensional finite element simulations performed using COMSOL Multiphysics®. Compared to the referential prismatic EANC, a significant augmentation in the pull-in displacement of the variable-width EANC has been obtained.

Establishing the peculiarities of tire wear of garbage trucks during the transportation of municipal solid waste

The article is dedicated to the establishment of peculiarities of tire wear of garbage trucks during the transportation of solid waste. Using the planning of the first-order experiment with the first-order interaction effects using the Box-Wilson method, adequate dependencies of wear of garbage truck tires on the front and rear axles due to the transported mass of municipal solid waste and the mileage of the garbage truck were determined. It was established that, according to the Student’s criterion, among the investigated factors of influence, the wear of garbage truck tires on both the front and rear axles is most affected by the transported mass of municipal solid waste, and the least – by the mileage of the garbage truck. The response surfaces of the objective functions – tire wear of the garbage truck on the front and rear axles and their two-dimensional sections in the planes of the impact parameters are shown, which allow to visually illustrate the indicated dependences of the objective function data on individual impact parameters. The dependencies of the number of routes of the garbage truck to the maximum allowable tire wear on the front and rear axles were obtained. The response surfaces of the target functions – the number of routes of the garbage truck to the maximum permissible wear of the tires on the front and rear axles and its two-dimensional sections in the planes of the influence parameters, which allow to visually illustrate the specified dependencies, are obtained. The expediency of conducting further research on the influence of speed, unevenness of the road surface, weather conditions and other factors on the wear of garbage truck tires has been revealed.

Effect of Aggregate on the Performance of Fly-Ash-Based Geopolymer Concrete

The influence of geopolymer binder characteristics on the performance of geopolymer concrete has been extensively investigated. Yet, the influence of aggregate properties has not been thoroughly studied, and it is usually assumed that their effect is the same as in cement concrete. This study investigates the effect of aggregate on the performance of fly-ash-based geopolymer concrete. A systematic experimental study was undertaken to investigate the effect of aggregate parameters, including volume fractions (AVFs), coarse aggregate to the total aggregate ratio (CAR), maximum coarse aggregate size (MAS), and fineness modulus of fine aggregate (FFM) on the compressive strength, slump, apparent volume of permeable pores (AVPPs), and the air content of geopolymer concrete. Response surface methodology (RSM) using the central composite design approach was utilized to design the experiments and analyze the results statistically. The analysis shows that all of the investigated aggregate parameters have significant first-order effects on the measured properties. No significant interaction between any of the investigated parameters was found. The aggregate may alter the geopolymerization processes, whereby SEM-EDS analysis revealed statistically significant variations in the elemental concentrations of the produced paste as the aggregate parameters changed. Quantitative weights were assigned to the effect of the investigated aggregate parameters on the measured properties. Multi-objective optimization was carried out to obtain the best combinations of the investigated parameters. Additionally, the developed contour graphs may provide an effective tool that can be used as a guide in establishing the first trial mixtures. A wide range of consistencies (10–210 mm slump) and compressive strengths (15–55 MPa) can be obtained by controlling the aggregate grading and proportions.

Research on the Influence of Digital Economy on Technological Innovation: Evidence from Manufacturing Enterprises in China

Digital economy is a key breakthrough in the new round of the industrial revolution, and technological innovation is the key to economic growth and wealth creation by enterprises. The influence of the digital economy on the innovation of manufacturing enterprises is directly related to solving the problem of inadequate development. Therefore, it is of great theoretical value and practical significance to study the influence of the digital economy on enterprise technological innovation. Taking Chinese manufacturing companies during 2016–2020 as a sample, this paper measured the technological innovation level of enterprises by the quantity and quality of innovation output of manufacturing enterprises and measured the development degree of the digital economy by the four dimensions of digital economy infrastructure, digital industrialization, industrial digitalization, and digital governance. The influence of the digital economy on enterprise technological innovation was researched through the Moran index and panel regression model. Moran’s indexes were all greater than 0, and the data were concentrated in the first and third quadrants of the scatter chart, and the value dropped from 0.186 to 0.152, indicating that provincial digital economic development presents a phenomenon of aggregation in spatial distribution, which gradually decreases along the eastern coast to the western region and gradually moves from aggregation to dispersion. The regression coefficients are significant at least at the level of 10%, indicating that the digital economy can effectively promote the output quantity and quality of technological innovation in manufacturing enterprises. The digital economy has a double-promotion effect on technological innovation. In promoting the technological innovation of manufacturing enterprises, infrastructure, digital industrialization, and industrial digitization play a dual and positive role as well as digital governance. In addition, the digital economy and its four dimensions have a first-order and second-order time-lag effect, which has a double-promotion effect on enterprises’ technological innovation. In general, the digital economy can promote enterprise technological innovation.

Pressure- and temperature-dependent klinkenberg slippage effect in porous media to non-ideal gases

The present paper evaluates the effect of non-ideal gas behavior on the Klinkenberg gas slippage effect for measuring the permeability of porous media. The generic cubic equation of state, particularly van der Waals (vdW-), Soave-Redlich-Kwong (SRK-), and Peng-Robinson (PR-) equation of state, are used to consider the non-ideal behavior of the gases, including nonhydrocarbons and hydrocarbons. The above cubic equation of state is expressed in terms of the gas compressibility factor involving the temperature-dependent second and third virial coefficients. A comprehensive mathematical model leading to a generalized analytical solution for the pressure- and temperature-dependent apparent permeability of porous media to non-ideal gas is proposed after combining the first-order Klinkenberg slippage effect and virial equation of state. Experimental data of Klinkenberg (1941) and Calhoun (1976) [Klinkenberg, L. J., The permeability of porous media to liquids and gases. Drill Prod Prac. API, 200–213, 1941; Calhoun, J. C., 1976. Fundamentals of Reservoir Engineering, University of Oklahoma Press, Oklahoma] are used to validate the proposed apparent permeability models. The proposed methodology accurately predicts the liquid permeability using the 18-test core samples and 7-test gases, accounting for the non-ideal behavior. The temperature-dependency of the apparent permeability of porous media to non-ideal gases with varying mean pressure is also established.

A comparative thermal case study on thermophysical aspects in thermally magnetized flow regime with variable thermal conductivity

It is well consensus among researchers affiliated with the field of thermal engineering that the thermophysical characteristics of heat transfer in fluid science own abundant applications like thermal distillation systems, heat exchangers, steam-electric power generation, electronic cooling, solar collectors, refrigeration systems and spacecraft thermal protection are to mention just a few. Considering such importance we offer a thermal case study on thermophysical aspects in a thermally magnetized non-Newtonian fluid along with a first-order chemical reaction effect. The flow field is carried with the following thermophysical effects namely, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent variable thermal conductivity. We have offered comparative analysis for temperature and Nusselt number by considering thermally radiative and non-radiative thermal flow fields. The thermal outcomes on temperature and Nusselt number are also reported for both the absence and presence of the heat generation effect. For both radiative and non-radiative Casson flow, the temperature shows an inciting nature towards Casson and variable thermal conductivity parameters. The magnitude of the Nusselt number towards Eckert, Prandt numbers, curvature, heat generation, and Casson fluid parameters is higher for the presence of thermal radiations while the opposite is the case for positive variation in the thermal conductivity parameter.

The effects of TV content on entrepreneurship: Evidence from German unification

This paper empirically analyzes whether television (TV) can influence individuals’ decisions to start businesses. To identify TV's effects, we rely on a unique quasi-natural experiment related to the division of Germany after WWII until 1990 into West Germany with a free market economy and the socialist East Germany where starting one's own business was not permitted. Despite this division, Western TV was exogeneously available since the 1960s in some, but not all East German regions and conveyed images and attitudes conducive to entrepreneurship. We use both regional-level and geo-referenced individual-level data and show that since starting a business in East Germany became possible thanks to the reunification in 1990, entrepreneurship incidence is higher in East German regions that had Western TV signal. This indicates a first-order effect on directly exposed individuals. We show that this is due to the effects of Western TV on attitudes and value orientations associated with entrepreneurship, particularly independence. We find no indication that the differences in the entrpreneurship incidence of East German regions with and without Western TV disappear. Instead, we find that successive cohorts and descendants of directly exposed individuals who were not directly exposed themselves more frequently wish to become entrepreneurs. The latter findings are consistent with second-order effects due to intergenerational transmission of an entrepreneurial mindset and suggest that a self-sustaining entrepreneurial culture can be formed. This can cause long-lasting differences between treated and non-treated population groups or regions.

Rethinking Vibrational Stark Spectroscopy: Peak Shifts, Line Widths, and the Role of Non-Stark Solvent Coupling

A vibration's transition frequency is partly determined by the first-order Stark effect, which accounts for the electric field experienced by the mode. Using ultrafast infrared pump-probe and FT-IR spectroscopies, we characterized both the 0 → 1 and 1 → 2 vibrational transitions' field-dependent peak positions and line widths of the CN stretching mode of benzonitrile (BZN) and phenyl selenocyanate (PhSeCN) in ten solvents. We present a theoretical model that decomposes the observed line width into a field-dependent Stark contribution and a field-independent non-Stark solvent coupling contribution (NSC). The model demonstrates that the field-dependent peak position is independent of the line width, even when the NSC dominates the latter. Experiments show that when the Stark tuning rate is large compared to the NSC (PhSeCN), the line width has a field dependence, albeit with major NSC-induced excursions from linearity. When the Stark tuning rate is small relative to the NSC (BZN), the line width is field-independent. BZN's line widths are substantially larger for the 1 → 2 transition, indicating a 1 → 2 transition enhancement of the NSC. Additionally, we examine, theoretically and experimentally, the difference in the 0 → 1 and 1 → 2 transitions' Stark tuning rates. Second-order perturbation theory combined with density functional theory explain the difference and show that the 1 → 2 transition's Stark tuning rate is ∼10% larger. The Stark tuning rate of PhSeCN is larger than BZN's for both transitions, consistent with the theoretical calculations. This study provides new insights into vibrational line shape components and a more general understanding of the vibrational response to external electric fields.

Modeling the relationship between digital nativity and Smartphone usage in learning English as a foreign language contexts.

Despite many studies exploring the application of digital devices in foreign language learning, only some have investigated the influencing mechanisms of digital nativity on Smartphone usage in this increasingly seamless learning environment. This research aims to explore the relationships between college students' digital nativity and their use of Smartphones for English learning. The data were collected from 502 undergraduates in mainland China through self-reported questionnaires, namely the Digital Natives Assessment Scale and the Smartphone Use in Learning Foreign Language Scale. The confirmatory factor analysis validated a four-factor measurement model of digital nativity, including "grow up with technology", "comfortable with multitasking", "reliant on graphics for communication" and "thrive on instant gratification and rewards". A second-order measurement construct of favorable Smartphone usage and its first-order adverse effects in foreign language learning were also examined, demonstrating good validity and reliability. Structural equation modeling analysis revealed that students who displayed more attributes of "grow up with technology" and "thrive on instant gratifications and rewards" tended to adopt smartphones positively for English learning. In addition, those who were more familiar with technological assistance might suffer less from the adverse effects of Smartphone usage. However, the preference for immediate responses and feedback could also lead to more adverse effects when using Smartphones for English learning. Besides, "comfortable with multitasking" and "reliant on graphics for communication" didn't have any significant predictive impact on either the favorable functions or the adverse effects of Smartphone usage. Based on the research results, we discuss the theoretical and practical implications.

Particle orientation distribution in a rotating, dilute suspension of rod-shaped particles

We consider a theoretical model for the settling of rod-shaped particles of a dilute, initially homogeneous, suspension in rapid rotation. The particle Reynolds number and the particle Taylor number of the detailed flow around the particles are assumed small, representing a relevant limit for an industrial centrifugal separation process. By applying a statistical approach using the Fokker–Planck equation, and neglecting particle–particle interactions, we obtain an explicit, analytical solution for the time dependent, spatially uniform particle orientation distribution function. Not only does the volume fraction in the bulk of the suspension decrease with time due to the divergent centrifugal field, as similarly described in the literature for suspensions of spherical particles, the orientation of the rod particles also changes with time from an initially uniform distribution to one where the particles tend to align with a plane perpendicular to the axis of rotation. The corresponding particle trajectories, as also influenced by first-order effects from the Coriolis acceleration and gyroscopic effects, are obtained numerically for different initial particle orientation angles.

Sensitivity analysis of geometric parameters on the aerodynamic performance of a multi-element airfoil

High-lift devices play a vital role in most commercial airplanes' design, maintenance, safety, and performance. The design of high-lift devices is complex due to the flow physics, actuation systems, geometry, and system support. Especially in a three-element high lift system, the position of the slat and flap significantly affects the aerodynamic performance. In this study, the sensitivity of aerodynamic quantities of the three-element airfoil to four geometric parameters was investigated using computational methods. In the sensitivity analysis, the Sobol sequence sampling method, the radial basis function, and Sobol's method were used to generate the sampling points in the given design space, to construct the metamodel, and evaluate the sensitivity indices, respectively. The sensitivity indices show that the slat overhang position is the largest contributor to the first-order and total effects. In general, it was shown that the forward elements play an important role in changing the flow behaviour of the trailing elements. Further, it was noted that the flap gap has the largest interaction effects on the lift and drag of the overall airfoil.

Nonlinear Model Predictive Control of J2-perturbed impulsive transfer trajectories in long-range rendezvous missions

This paper develops a Nonlinear Model Predictive Control (NMPC) strategy for robust tracking of multi-impulse smooth transfer trajectories in J2-perturbed orbital environments. The reference trajectories are designed for long-range rendezvous of servicing satellites with orbiting targets. In the proposed NMPC, the control signals are velocity increments at the impulse times, and the prediction horizon is variable due to the impulsive nature of the reference trajectories. The reference control input and the impulse times are pre-specified by the reference trajectory. Then, the NMPC calculates the optimal correction control vector to track the trajectory with minimum deviation and control effort, during the time between two consecutive impulses. To arrive near the target at the end of the transfer, the optimization in the last horizon is modified to be free-final-time, with an added soft constraint to minimize the final distance between the servicer and the target satellite. To avoid singularities in the mean dynamics of the J2-perturbed servicer, the equinoctial orbital elements are used in the process model. We also include the first-order long-periodic effects in this model. We investigate the robustness of the proposed NMPC in a simulation environment that additionally models: (i) the first-order short-periodic effects, (ii) a bounded uncertain acceleration to capture unmodelled dynamics, and (iii) burning time for satellite thrusters. Finally, an evolutionary optimization algorithm is implemented and embedded in the controller to decrease the computational complexity and to handle impulsive control inputs. Simulation results are provided to illustrate the tracking effectiveness of the developed controller.

Modelling the propagation of infectious disease via transportation networks

The dynamics of human mobility have been known to play a critical role in the spread of infectious diseases like COVID-19. In this paper, we present a simple compact way to model the transmission of infectious disease through transportation networks using widely available aggregate mobility data in the form of a zone-level origin-destination (OD) travel flow matrix. A key feature of our model is that it not only captures the propagation of infection via direct connections between zones (first-order effects) as in most existing studies but also transmission effects that are due to subsequent interactions in the remainder of the system (higher-order effects). We demonstrate the importance of capturing higher-order effects in a simulation study. We then apply our model to study the first wave of COVID-19 infections in (i) Italy, and, (ii) the New York Tri-State area. We use daily data on mobility between Italian provinces (province-level OD data) and between Tri-State Area counties (county-level OD data), and daily reported caseloads at the same geographical levels. Our empirical results indicate substantial predictive power, particularly during the early stages of the outbreak. Our model forecasts at least 85% of the spatial variation in observed weekly COVID-19 cases. Most importantly, our model delivers crucial metrics to identify target areas for intervention.

Second-order topological magneto-optical effects in noncoplanar antiferromagnets

The second-order magneto-optical effects, represented by Voigt and Sch\"{a}fer-Hubert effects, are effective methods to detect the spin textures in antiferromagnets, whereas the previous studies are usually limited to collinear antiferromagnets. In noncollinear antiferromagnets, the spin textures characterized by spin chirality have been revealed to play a critical role in many exciting physics. In particular, the first-order topological magneto-optical effects originated from scalar spin chirality have been discovered recently. In this work, using the first-principles calculations and group theory analysis, we generalize the first-order topological magneto-optical effects to the second-order cases, that is, topological Voigt and Sch\"{a}fer-Hubert effects, by taking the noncoplanar 3Q spin state of $\gamma$-Fe$_{x}$Mn$_{1-x}$ alloy as an example. The conventional Voigt and Sch\"{a}fer-Hubert effects are comparatively studied in the collinear 1Q and 2Q spin states of $\gamma$-Fe$_{x}$Mn$_{1-x}$ alloy. In addition, the natural linear birefringence due to crystal anisotropy is discussed in the strained 1Q, 2Q, and 3Q states, and a unique fingerprint for experimentally distinguishing the second-order topological magneto-optical effects and natural linear birefringence is identified. Our work brings a topological insight into the second-order magneto-optical effects in noncoplanar antiferromagnets and also provides $\gamma$-Fe$_{x}$Mn$_{1-x}$ as an attractive material platform for future experimental exploration.

Prescribed Fire First-Order Effects on Oak and Maple Reproduction in Frequently Burned Upland Oak–Hickory Forests of the Arkansas Ozarks

Alteration of the fire regime in upland oak–hickory (Quercus L. spp.–Carya Nutt. spp.) forests of the Central Hardwood Region is a major factor for the current shifts in species’ composition and oak recruitment and regeneration failures. The reintroduction of fire into these ecosystems requires a better understanding of fire effects on oak and co-occurring competitors. First-order (i.e., during and immediately after) fire effects on oak and red maple (Acer rubrum L.) topkill and resprouting at neighborhood scales were evaluated in frequently burned upland oak–hickory forests. A groundline threshold of 5 cm provided oaks with high (60%) survival probability (p < 0.001). White (Quercus alba L.) and post (Quercus stellata Wangenh.) oak survival odds were 21 and 14 times higher than that of red maple (p = 0.01 and 0.03), respectively. Three and twelve months after burn, oaks had three to six times more sprouts per clump than red maple. Frequent fires may continue to topkill the maples, while maintaining oak dominance in the reproduction pool and, thus, providing higher recruitment potential into the overstory. Burns with fire behavior that is very low to low in these frequently burned systems may provide greater control in favoring oaks and selecting against red maple, especially if groundline diameter thresholds are considered.

From ridges to manifolds: 3D characterization of the moving groups in the Milky Way disc

Context. The details of the effect of the bar and spiral arms on the disc dynamics of the Milky Way are still unknown. The stellar velocity distribution in the solar neighbourhood displays kinematic substructures, which are possibly signatures of these processes and of previous accretion events. With the Gaia mission, more details of these signatures, such as ridges in the Vϕ − R plane and thin arches in the Vϕ − VR plane, have been revealed. The positions of these kinematic substructures, or moving groups, can be thought of as continuous manifolds in the 6D phase space, and the ridges and arches as specific projections of these manifolds. Aims. Our aim is to detect and characterize the moving groups along the Milky Way disc, sampling the galactocentric radial and azimuthal velocities of the manifolds through the three dimensions of the disc: radial, azimuthal, and vertical. Method. We developed and applied a novel methodology to perform a blind search for substructure in the Gaia EDR3 6D data, which consists in the execution of the wavelet transform in independent small volumes of the Milky Way disc, and the grouping of these local solutions into global structures with a method based on the breadth-first search algorithm from graph theory. We applied the same methodology to simulations of barred galaxies to validate the method and for comparison with the data. Results. We reveal the skeleton of the velocity distribution, uncovering projections that were not possible before. We sample nine main moving groups along a large region of the disc in configuration space, covering up to 6 kpc, 60 deg, and 2 kpc in the radial, azimuthal, and vertical directions, respectively, extending significantly the range of previous analyses. In the radial direction we find that the groups deviate from the lines of constant angular momentum that one would naively expect from an epicyclic approximation analysis of the first-order effects of resonances. We reveal that the spatial evolution of the moving groups is complex and that the configuration of moving groups in the solar neighbourhood is not maintained along the disc. We also find that the azimuthal velocity of the moving groups that are mostly detected in the inner parts of the disc (Arcturus, Bobylev, and Hercules) is non-axisymmetric. For Hercules we measure an azimuthal gradient of −0.50 km s−1 deg−1 at R = 8 kpc. We detect a vertical asymmetry in the azimuthal velocity for the Coma Berenices moving group, which is not expected for structures originating from a resonance of the bar, supporting the previous hypothesis of the incomplete vertical phase mixing of the group. In our simulations we extract substructures corresponding to the outer Lindblad resonance and the 1:1 resonances and observe the same deviation from constant angular momentum lines and the non-axisymmetry of the azimuthal velocities of the moving groups in the inner part of the disc. Conclusions. This data-driven characterization is a starting point for a holistic understanding of the moving groups. It also allows for a quantitative comparison with models, providing a key tool to comprehend the dynamics of the Milky Way.

Children and Retirement Income Adequacy

A typical household spends about $13,000 per year providing each child with food, clothing, shelter, and other essentials of life, with parental expenditures on children totaling 5% of gross domestic product. Several studies have shown that how children are assumed to interact with household expenditures and saving has first-order effects on judgments of the adequacy of retirement saving by US households, yet the effect of children on their parents’ ability and need to save for retirement is unresolved. This article uses data from the Panel Study of Income Dynamics (PSID) to track changes in household spending and saving as children transition to financial independence and parents’ transition from work into retirement. The PSID data accord with an interpretation of the life-cycle model in which parental households consume more and save less during the period children are being raised, but reduce consumption and increase saving as children become economically independent. These results point toward a more optimistic picture of the adequacy of US household retirement savings.

Temperature distribution in a laser-heated diamond anvil cell as described by finite element analysis

Finite element analysis (FEA) is a powerful tool for numerically solving partial differential equations over complex geometries and is thus useful for analyzing heat transport in laser-heated diamond anvil cell (LHDAC) experiments. Our models expand on previously published simulations by calculating the volume-averaged temperatures of both the sample and insulation/pressure media under steady-state heating to determine the thermal pressure of the hot sample. Our goal is to produce an accurate relationship between the measured surface temperature of the absorbing sample and the temperature of the transparent insulating media, which is used to determine thermal pressure but susceptible to steep temperature gradients. We find that in doing so, our FEA models of temperature within the pressure/insulation media can differ from simplified estimates of temperature gradients by more than a factor of 2. We also explore temperature-dependent and temperature-independent thermal conductivity models and find that the volume-averaged temperatures differ by up to a factor of 1.3, forcing the predicted thermal pressures determined to also differ by up to a factor of 1.5 at a temperature of 2000 K at 50 GPa for neon. Higher temperatures exacerbate this difference. We also find that unintentional asymmetric sample insertion and sample heating, which are common in LHDAC experiments, do not have a first-order effect on volume-averaged temperatures. The FEA models, available in both Python and FlexPDE, are versatile across different sample geometries, materials, and heat source laser shapes.