Small Values Research Articles

Texture Analysis of Temporomandibular Joint Disc Changes Associated with Effusion Using Magnetic Resonance Images.

A total of 223 images of the TMJ, 42 with joint effusion and 181 without, were analyzed. Three consecutive slices were then exported to MaZda software, in which two oval ROIs (one in the anterior band and another in the intermediate zone of the joint disc) were determined in each slice and eleven texture parameters were calculated by using a gray-level co-occurrence matrix. Spearman's correlation coefficient test was used to assess the correlation between texture variables and to select variables for analysis. The Mann-Whitney test was used to compare the groups. The significance level was set at 5%, with the results demonstrating that there was no high correlation between the parameter directions. It was possible to observe a trend between the average parameters, in which the group with effusion always had smaller values than the group without effusion, except for the parameter measuring the difference in entropy. The trend towards lower overall values for the texture parameters suggested a different behavior between TMJ discs affected by effusion and those not affected, indicating that there may be intrinsic changes.

Elementar həndəsədə optimallaşdırma məsələləri və onların funksional metodla araşdırılması

In the study of extremes in elementary geometry, the functional method is mainly used. To do this, an independent variable (argument) is first selected and the geometric process is described as a function depending on this argument. Then elements of differential calculus are used. Thus, with the help of derivatives, the properties of functions are investigated-their stability, monotonicity, the points of its extremes, the largest and smallest values. Practically, textbooks and textbooks on elementary mathematics pay little attention to these issues. Therefore, in this article, the solution of the problems of extremum geometry was studied using derivatives in theoretical and practical aspects. The article is relevant for specialists, teachers, students and schoolchildren engaged in elementary mathematics.

Naturalistic study of vehicle-bicycle lateral passing distance on high-speed rural two-lane roadways with paved shoulders

In the United States, 91.4 cm (3.0 ft) has been considered a safe lateral distance when passing bicyclists; however, this threshold may be more suitable to urban environments where most bicycle safety research has originated—limited research is available on rural roadways. In this study, a road bicycle was instrumented to collect naturalistic data and analyze vehicle-bicycle lateral passing distances (LPD) on high-speed rural two-lane roadways with paved shoulders. The bicycle was ridden in the center of the shoulder. Overall, 2,119 observations of vehicles passing the instrumented bicycle were obtained from a study segment. The impacts of different variables on distributions of vehicle-bicycle LPD measurements were analyzed. Passing vehicles with opposing traffic passed the bicyclist significantly closer than passing vehicles without opposing traffic. More predominant with opposing traffic, heavy vehicles passed the bicyclist closer than passenger vehicles. Similarly, following vehicles passed the bicyclist closer than leading vehicles. The study segment was repaved during the data collection period, so data before and after the roadway improvement was available. Vehicles with old pavement/marking passed the bicyclist closer than vehicles with new pavement/marking conditions. Distribution of LPD measurements was skewed to the left towards smaller values and had a long tail to the right towards larger values. Through maximum likelihood estimation, the Log-normal distribution was found to best fit the data distribution. Using empirical and theoretical density distributions, LPD was formally specified as a function of opposing traffic with a theoretical mixture distribution and generalized to estimate the probability of vehicles passing bicyclists below a certain threshold.

Delayed Detached-Eddy Simulations of Rough-Wall Turbulent Reactive Flows in a Supersonic Combustor

Reactive delayed detached-eddy simulations (DDESs) of hydrogen injection into a confined transverse supersonic flow of vitiated air are conducted. The corresponding conditions were studied in the LAPCAT-II combustor, which—due to thermal coating—exhibits non-negligible wall roughness. Its effects are taken into account with the equivalent sand-grain roughness model, and, to the best of the authors’ knowledge, it is the first time that this modeling framework is considered within the DDES framework to simulate turbulent reactive flows. Two operating conditions are considered, which differ in the value of the momentum ratio between the hydrogen and vitiated air inlet streams, thus leading to two distinct values of the operating equivalence ratio (ER). For its smallest value, smooth combustion is subject to a preliminary thermal runaway period, while for its largest value, combustion is more strongly intertwined with shock wave dynamics and boundary-layer separation. Since it features large subsonic regions, which are characteristic of situations close to thermal choking, the latter is referred to as the sudden or partially choked combustion mode. Computational results are assessed through comparisons with available experimental data for both operating conditions. The main mechanism through which wall roughness alters the combustion development lies in the reduction of the effective cross-sectional area that is induced by boundary-layer thickening. For the largest ER value, DDES conducted with the sand-grain roughness model does recover the partially choked combustion mode, while smooth wall (i.e., standard) DDES does not.

Terminal Embeddings in Sublinear Time

Recently (Elkin, Filtser, Neiman 2017) introduced the concept of a {\it terminal embedding} from one metric space $(X,d_X)$ to another $(Y,d_Y)$ with a set of designated terminals $T\subset X$. Such an embedding $f$ is said to have distortion $\rho\ge 1$ if $\rho$ is the smallest value such that there exists a constant $C>0$ satisfying \begin{equation*} \forall x\in T\ \forall q\in X,\ C d_X(x, q) \le d_Y(f(x), f(q)) \le C \rho d_X(x, q) . \end{equation*} When $X,Y$ are both Euclidean metrics with $Y$ being $m$-dimensional, recently (Narayanan, Nelson 2019), following work of (Mahabadi, Makarychev, Makarychev, Razenshteyn 2018), showed that distortion $1+\epsilon$ is achievable via such a terminal embedding with $m = O(\epsilon^{-2}\log n)$ for $n := |T|$. This generalizes the Johnson-Lindenstrauss lemma, which only preserves distances within $T$ and not to $T$ from the rest of space. The downside of prior work is that evaluating their embedding on some $q\in \mathbb{R}^d$ required solving a semidefinite program with $\Theta(n)$ constraints in~$m$ variables and thus required some superlinear $\mathrm{poly}(n)$ runtime. Our main contribution in this work is to give a new data structure for computing terminal embeddings. We show how to pre-process $T$ to obtain an almost linear-space data structure that supports computing the terminal embedding image of any $q\in\mathbb{R}^d$ in sublinear time $O^* (n^{1-\Theta(\epsilon^2)} + d)$. To accomplish this, we leverage tools developed in the context of approximate nearest neighbor search.

Entropy-based analysis of hemodynamics in elliptical arterial flows with non-Newtonian Rabinowitsch fluid

This research concerns examining the non-Newtonian blood flow behavior through an artery of elliptic cross-section, affected by several stenoses. The Rabinowitsch fluid model is used to investigate the non-Newtonian behavior of the blood for uniform and nonuniform shapes of stenosis. The mathematical equations have been converted into a dimensionless form, and their nonlinearity is reduced by applying the assumptions of mild stenosis. The resulting differential equations are solved by using analytical techniques. A new polynomial of degree eight is introduced to complete the solutions of mathematical equations. The entropy generation is studied mathematically to analyze the irreversibility effects. The detailed graphical examination delineates the physical aspects of mathematical results. The flow velocity is higher for uniform shape than for nonuniform stenosis. The rising percentage of stenosis significantly enhances the flow velocity of the stenotic region. The entropy is enormous near the stenotic wall and has small values near the centerline, which assures the smooth flow in this region. Further, the streamlines are plotted to find the position of stenosis and assess the flow nature for the growing height of stenosis and rising flow rate.

Extremely Monodispersed Micrometer-Scale Spherical Particle Synthesis of Ag Inside a Microdroplet Vaporizing in Plasma.

Spherical Ag particles have received considerable attention because of their unique properties as well as their applications in various fields. In the present study, the synthesis of micrometer-scale spherical Ag particles with an extremely narrow size distribution is demonstrated using a simple capacitively coupled atmospheric-pressure plasma reactor with an inkjet head. Droplets of a Ag nitrate aqueous solution are ejected from the inkjet head to synthesize Ag particles. The gaseous temperature in the reactor is adjusted such that Ag can be melted with a negligibly small vapor pressure. These particles exhibit a spherical shape with a smooth surface. The mean diameter of the particles is 0.91 ± 0.013 μm with a small coefficient of variation of 1.5%, the smallest value ever reported for Ag particles of less than 1 μm. The grain sizes of the particles are larger than 100 nm, as expected from the broadening of the X-ray diffraction peaks. The excellent monodispersity of the particles synthesized by this method may expand the applications with micrometer-scale spheres such as ball spacer, microsized ball bearing, and inks for printed electronics.

Derivation of the Schrödinger equation from QED

The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.

Stable production of fluid jets with vanishing diameters via tip streaming

We study numerically the microjetting mode obtained when a fluid is injected through a tube submerged in a uniaxial extensional flow. The steady solution to the full nonlinear Navier–Stokes equations is calculated. We obtain the linear global modes determining the linear stability of the steady solution. For sufficiently large outer viscosity, the flow remains stable for infinitely small values of the injected flow rate. This implies that jets with vanishing diameters can be produced regardless of the jet viscosity and outer flow strength. For a sufficiently small inner-to-outer viscosity ratio, the microjetting instability is associated only with the flow near the entrance of the jet. The tapering meniscus stretches and adopts a slender quasiconical shape. Consequently, the cone tip is exposed to an intense outer flow, which stabilizes the flow in the cone–jet transition region. This work presents the first evidence that fluid jets with arbitrarily small diameters can be stably produced via tip streaming. The results are related to those of a droplet in a uniaxial extensional flow with its equator pinned to an infinitely thin ring. The pinning of the equator drastically affects the droplet stability and breakup.

Replica analysis of overfitting in regression models for time to event data: the impact of censoring

We use statistical mechanics techniques, viz. the replica method, to model the effect of censoring on overfitting in Cox’s proportional hazards model, the dominant regression method for time-to-event data. In the overfitting regime, Maximum Likelihood (ML) parameter estimators are known to be biased already for small values of the ratio of the number of covariates over the number of samples. The inclusion of censoring was avoided in previous overfitting analyses for mathematical convenience, but is vital to make any theory applicable to real-world medical data, where censoring is ubiquitous. Upon constructing efficient algorithms for solving the new (and more complex) Replica Symmetric (RS) equations and comparing the solutions with numerical simulation data, we find excellent agreement, even for large censoring rates. We then address the practical problem of using the theory to correct the biased ML estimators without knowledge of the data-generating distribution. This is achieved via a novel numerical algorithm that self-consistently approximates all relevant parameters of the data generating distribution while simultaneously solving the RS equations. We investigate numerically the statistics of the corrected estimators, and show that the proposed new algorithm indeed succeeds in removing the bias of the ML estimators, for both the association parameters and for the cumulative hazard.

Combustion Characteristics of a Hydrogen-Fueled TJI Engine under Knocking Conditions

The use of a two-stage combustion system in a hydrogen-fueled engine is characteristic of modern internal combustion engines. The main problem with hydrogen combustion in such systems is knocking combustion. This paper contains the results of research under knock combustion conditions with a single-cylinder internal combustion engine equipped with a turbulent jet ignition system (TJI). A layout with a passive pre-chamber and a variable value of the excess air ratio range λ = 1.25–2.0 with a constant value of the center of combustion (CoC = 4 deg) after top dead center (TDC) was used. Two indicators of knock combustion were analyzed: maximum oscillation of pressure and the Mahle Knock Index. Analyses were also carried out taking into account the rate of heat release and the amount of heat released. As a result of the investigation, it was found that knock combustion occurs intensively at small values of the air excess ratio. Hydrogen knock combustion disappears for λ = 2.0 and greater. The pressure oscillation index was found to be more applicable, as its limiting value (>1 bar) allows easy diagnosis of knock combustion. The Mahle Knock Index is a quantity that allows interval analysis of the knock. The choice of classes and weighting coefficients requires an iterative operation, as they strictly depend on engine characteristics, load, and knock magnitude.

Horizontal sound localization in presence of noise in normal-hearing young adults

Objective: This study investigates the effect of signal-to-noise ratio (SNR), frequency, and bandwidth on horizontal sound localization accuracy in normal-hearing young adults. Methods: From August 2022 to December 2022, a total of 20 normal-hearing young adults, including 7 males and 13 females, with an age range of 20 to 35 years and a mean age of 25.4 years, were selected to participate in horizontal azimuth recognition tests under both quiet and noisy conditions. Six narrowband filtered noise stimuli were used with central frequencies (CF) of 250, 2 000, and 4 000 Hz and bandwidths of 1/6 and 1 octave. Continuous broadband white noise was used as the background masker, and the signal-to-noise ratio (SNR) was 0, -3, and -12 dB. The root-mean-square error (RMS error) was used to measure sound localization accuracy, with smaller values indicating higher accuracy. Friedman test was used to compare the effects of SNR and CF on sound localization accuracy, and Wilcoxon signed-rank test was used to compare the impact of the two bandwidths on sound localization accuracy in noise. Results: In a quiet environment, the RMS error in horizontal azimuth in normal-hearing young adults ranged from 4.3 to 8.1 degrees. Sound localization accuracy decreased with decreasing SNR: at 0 dB SNR (range: 5.3-12.9 degrees), the difference from the quiet condition was not significant (P>0.05); however, at -3 dB (range: 7.3-16.8 degrees) and -12 dB SNR (range: 9.4-41.2 degrees), sound localization accuracy significantly decreased compared to the quiet condition (all P<0.01). Under noisy conditions, there were differences in sound localization accuracy among stimuli with different frequencies and bandwidths, with higher frequencies performing the worst, followed by middle frequencies, and lower frequencies performing the best, with significant differences (all P<0.01). Sound localization accuracy for 1/6 octave stimuli was more susceptible to noise interference than 1 octave stimuli (all P<0.01). Conclusions: The ability of normal-hearing young adults to localize sound in the horizontal plane in the presence of noise is influenced by SNR, CF, and bandwidth. Noise with SNRs of ≥-3 dB can lead to decreased accuracy in narrowband sound localization. Higher CF signals and narrower bandwidths are more susceptible to noise interference.

On Item-Sampling Evaluation for Recommender System

Personalized recommender systems play a crucial role in modern society, especially in e-commerce, news, and ads areas. Correctly evaluating and comparing candidate recommendation models is as essential as constructing ones. The common offline evaluation strategy is holding out some user-interacted items from training data and evaluating the performance of recommendation models based on how many items they can retrieve. Specifically, for any hold-out item or so-called target item for a user, the recommendation models try to predict the probability that the user would interact with the item and rank it among overall items, which is called global evaluation . Intuitively, a good recommendation model would assign high probabilities to such hold-out/target items. Based on the specific ranks, some metrics like Recall@K and NDCG@K can be calculated to further quantify the quality of the recommender model. Instead of ranking the target items among all items, Koren first proposed to rank them among a small sampled set of items , then quantified the performance of the models, which is called sampling evaluation . Ever since then, there has been a large amount of work adopting sampling evaluation due to its efficiency and frugality. In recent work, Rendle and Krichene argued that the sampling evaluation is “inconsistent” with respect to a global evaluation in terms of offline top- K metrics. In this work, we first investigate the “inconsistent” phenomenon by taking a glance at the connections between sampling evaluation and global evaluation. We reveal the approximately linear relationship between sampling with respect to its global counterpart in terms of the top- K Recall metric. Second, we propose a new statistical perspective of the sampling evaluation—to estimate the global rank distribution of the entire population. After the estimated rank distribution is obtained, the approximation of the global metric can be further derived. Third, we extend the work of Krichene and Rendle, directly optimizing the error with ground truth, providing not only a comprehensive empirical study but also a rigorous theoretical understanding of the proposed metric estimators. To address the “blind spot” issue, where accurately estimating metrics for small top- K values in sampling evaluation is challenging, we propose a novel adaptive sampling method that generalizes the expectation-maximization algorithm to this setting. Last but not least, we also study the user sampling evaluation effect. This series of works outlines a clear roadmap for sampling evaluation and establishes a foundational theoretical framework. Extensive empirical studies validate the reliability of the sampling methods presented.

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems.

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

Sublinear drag regime at mesoscopic scales in viscoelastic materials.

Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Although exponential responses are the most common, power-law time dependencies arise peculiarly in complex soft materials such as living cells. Understanding the microscale mechanisms that drive rheologic behaviors at the macroscale shall be transformative in fields such as material design and bioengineering. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. The macromolecules, represented by particles in the network, interact with neighbors through a spring constant k and with fluid through a non-linear drag regime. The dissipative force is given by γvα, where v is the particle's velocity, and γ and α are mesoscopic parameters. Physically, the sublinear regime of the drag forces is related to micro-deformations of the macromolecules, while α ≥ 1 represents rigid cases. We obtain exponential or power-law relaxations or a transitional behavior between them by changing k, γ, and α. We find that exponential decays are indeed the most common behavior. However, power laws may arise when forces between the macromolecules and the fluid are sublinear. Our findings show that in materials not too soft not too elastic, the rheological responses are entirely controlled by α in the sublinear regime. More specifically, power-law responses arise for 0.3 ⪅ α ⪅ 0.45, while exponential responses for small and large values of α, namely, 0.0 ⪅ α ⪅ 0.2 and 0.55 ⪅ α ⪅ 1.0.

Radiological Measurement of Sella Turcica Dimensions in Different Skeletal Patterns in Romanian Patients

(1) Background: The purpose of this study was to evaluate the morphology and linear dimensions of sella turcica in Romanian participants from all three skeletal classes to see whether there were any differences. (2) Method: We examined 90 lateral cephalometric radiographs of patients aged 12 and older and divided them into skeletal classes I, II, and III (30 participants in each). Sella turcica linear measurements such as length, depth, and anteroposterior diameter were measured and studied. To see the nature of our data, Q–Q plots tests were performed. By examining these tests performed for each variable belonging to a particular class, it can be noted that the points are fairly well distributed along some lines, meaning that the data are normally distributed. An Anova test with Bonferroni correction was used to compare the mean values of the examined parameters between the classes. Also, to observe the correlation between our experimental data, the Pearson correlation coefficient was calculated. (3) Results: In all three skeletal classes, the average length of the sella was 8.98 mm ± 1.470, the average depth was 7.99 mm ± 1.081, and the average diameter was 10.29 mm ± 1.267. For all examined linear dimensions, there was a statistically significant difference between class I and class III subjects and between class II and class III subjects (p &lt; 0.001). The morphology of sella turcica was found to be normal in 51.1% of instances, representing the majority across all skeletal classes. In the Romanian population, sella turcica has shown a significant amount of variation. Class III subjects had larger sella dimensions, whereas class II subjects had smaller values. (4) Conclusions: The measurements and morphology of the sella analysed in the present research can serve as standards for subsequent research concerning the sella turcica region in individuals from Romania.

Understanding the role of perforations on the local hydrodynamics of gas–liquid flows through structured packings

Structured packings are widely used to perform gas–liquid separation processes as they provide a large mass-transfer area and low-pressure drop. The overall performance of these packings is governed by the local liquid distribution/gas–liquid interfacial area. The local liquid distribution is substantially influenced by the arrangement and geometrical features of the structured packing. While the influence of arrangement and few geometrical features on the local liquid distribution has recently been investigated using the structure-resolved simulations, the perforations on the structured packings are usually ignored. In the present work, we have performed structure-resolved gas–liquid flow simulations, using the Volume-of-Fluid (VOF) method implemented in the open-source C++ library OpenFOAM, in a periodic domain of Mellapak.250 with and without resolving the perforations. We show that the presence of perforations results in flow separation as well as droplet formation leading to an increase in the liquid holdup, interfacial and wetted areas, irrespective of the fluid properties and wetting conditions (specified using static contact angle ‘θw’) considered in this work. We also show that at an inclination angle ‘β’ of 45° from horizontal, the location of the perforations governs the local liquid distribution and the resulting flow metrics. However, at a β of 90°, the number of perforations governs the local liquid distribution, irrespective of their location. Further, we also show that the predictions of structure-resolved VOF simulations, with perforations resolved, are in a relatively better agreement with the correlations in the literature at small values of θw in terms of liquid holdup and interfacial area.

Extraction of geometric features and analysis of flow mechanism of high loaded compressor airfoils at low Reynolds number

When the aircraft cruising at high altitude, the aerodynamic performance of the compressor sharply decreases due to the enhanced boundary layer separation loss. Therefore, it is of great significance to design the high-performance airfoils suitable for low Reynolds numbers (Re) to improve the aerodynamic performance of compressor. In this paper, numerical simulations were carried out on a high-loaded subsonic compressor cascade V103 at low Re. Meanwhile, a multi-objective optimization of blade profile was performed to get optimal solutions, and data mining techniques were applied to extract valuable design knowledge from the optimal database. The results show that the Pareto-optimal airfoils achieve a maximum reduction of 27.32% in total pressure loss coefficient under design condition and 36.71% under near stall condition. Compared with the original airfoil, the curvature distribution law of the camber line with larger values at both ends and smaller values in the middle is advantageous for the performance of the compressor cascade under design condition. This distribution pattern causes a forward shift for the loading distribution of airfoils, accompanied by an earlier transition onset. Additionally, it reduces adverse pressure gradient at the rear part of suction surface, which suppresses the development and growth of laminar separation bubble and delays the separation of turbulent boundary layer. Under near stall condition, maintaining larger leading edge angle and uniform flow diffusion is beneficial for improving the performance of compressor cascade. This is because the larger leading edge angle reduces incidence angle, while the uniform flow diffusion inhibits a great flow separation.

Spatial resolution effects on the solar open flux estimates

Context. Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. Aims. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. Methods. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630 nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. Results. The results show a significant decrease in the mean magnetic flux density – related to the open flux observed at the disk center – with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20 cm aperture telescope yields a 30% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Conclusions. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle.

Analysis of the heat collection performance of a capillary solar heat collection wall structure

Solar thermal utilization in high-rise buildings is often constrained by the limited surface area of the rooftop. A novel façade-integrated capillary solar heat collection wall structure was proposed in this study, which involves embedding capillary tubes that circulate water within the cement mortar material, facilitating the integration of solar thermal collector and the exterior walls. To validate the feasibility of this new type of heat collection structure, experiments were conducted to investigate the impact of water flow rates on the heat collection performance of the proposed capillary solar heat collection wall structure under indoor solar simulator conditions, and outdoor field testing were conducted to assess its heat collection performance during winter, spring, and summer in Nanjing city. The experimental results revealed that, at water flow velocities of 0.05 m/s, 0.10 m/s, 0.15 m/s, and 0.20 m/s, the system's heat collection reached 4721 kJ, 4833 kJ, 4872 kJ, and 5326 kJ, respectively, showing a consistent increase with higher flow velocities in the capillary tube. The heat collection efficiency also increased gradually with flow velocity, but the rate of increase was relatively slow. The instantaneous heat collection efficiency decreased gradually as the experiment progressed, with a relatively small value of 47 % at a flow rate of 0.05 m/s. Data fitting revealed a linear relationship between the instantaneous collector efficiency and the normalized temperature difference at water flow velocities of 0.05 m/s and 0.1 m/s, and a quadratic exponential relationship at water flow velocities of 0.15 m/s and 0.2 m/s. During winter, spring, and summer in Nanjing city, the effective heat collection efficiency reached 45.8 %, 40.4 %, and 39.5 %, respectively, demonstrating that the capillary solar heat collection wall structure has significant potential in subtropical regions like Nanjing.