Two-dimensional Model Research Articles

2D capsid formation within an oscillatory energy landscape: orderly self-assembly depends on the interplay between a dynamic potential and intrinsic relaxation times.

Multiple dissipative self-assembly protocols designed to create novel structures or to reduce kinetic traps have recently emerged. Specifically, temporal oscillations of particle interactions have been shown effective at both aims, but investigations thus far have focused on systems of simple colloids or their binary mixtures. In this work, we expand our understanding of the effect of temporally oscillating interactions to a two-dimensional coarse-grained viral capsid-like model that undergoes a self-limited assembly. This model includes multiple intrinsic relaxation times due to the internal structure of the capsid subunits and, under certain interaction regimes, proceeds via a two-step nucleation mechanism. We find that oscillations much faster than the local intrinsic relaxation times can be described via a time averaged inter-particle potential across a wide range of interaction strengths, while oscillations much slower than these relaxation times result in structures that adapt to the attraction strength of the current half-cycle. Interestingly, oscillation periods similar to these relaxation times shift the interaction window over which orderly assembly occurs by enabling error correction during the half-cycles with weaker attractions. Our results provide fundamental insights to non-equilibrium self-assembly on temporally variant energy landscapes.

Two-dimensional model in a laminar flow slit photoreactor for the determination of surface kinetic constants considering the presence of diffusion limitations

Narrow slit reactors are widely used in laboratory testing of photocatalytic materials, as well as for the determination of kinetic coefficients in surface photocatalyzed reactions. In this work, the behavior of a continuous laminar flow slit reactor was described by a two-dimensional model, addressing the advection–diffusion problem in the fluid phase, coupled with a first-order chemical reaction on the reactor walls. The concentration profile of the reactant, in the transverse and longitudinal directions of the reactor, depends on two parameters that characterize the system; the Péclet number and the Damköhler number, in addition to the geometry of the reactor. Once a short distance from the reactor’s entrance has been surpassed, the relationship between the transversally averaged reactant concentration and the concentration existing on the catalytic surface becomes essentially constant, thus defining an (external) effectiveness factor. The simulations carried out for a wide range of values of the parameters characterizing the model showed that the effectiveness factor only depends on the Damköhler number, being independent of the value of the Péclet number and of the relationship between the reactor length and the distance separating the plates. An analytical expression for the effectiveness factor as a function of the Damköhler number was proposed, which allows to determine the value of the kinetic coefficient for the surface reaction (ks), even in the presence of important limitations to mass transfer. The methodology proposed was illustrated performing experiments of photocatalytic oxidation of toluene in air (with Péclet numbers ranging from 20 to 40), employing a paint formulated with carbon-doped TiO2 in a continuous laboratory photoreactor of flat parallel plates. The observed toluene conversions were in the range of 13 to 26 %, consequently, the calculated Damköhler number was Da = 0.0307 and the surface kinetic coefficient thus determined (for 50 % of relative humidity and 42.3 W/m2 of irradiance flux) was ks = 1.262 10-4 m/s. The significance of this work lies in the development of a comprehensive model that can be used to know the surface kinetics in photocatalytic reactions, applicable to scenarios where there are considerable mass transfer limitations or not

Numerical investigation on dynamic flow characteristics of methane condensation in microchannels

Microchannel condensers play an essential role in cryogenic two-phase heat management systems due to their efficient heat transfer characteristics. Thus, it is worth conducting an in-depth study on microscale condensation characteristics of cryogenic fluids. This paper delves into the flow condensation process of methane in microchannels. A two-dimensional transient model with high accuracy for cryogenic fluids has been developed by combining a self-defined program for the source term of the phase transition model. The model fully considers the boundary layer thickness and accurately explores the mesh accuracy. The complete condensation flow patterns are captured for various vapor quality, mass flux, and wall subcooling degrees. The injection flow is a unique flow regime for condensation in microchannels. The decrease in wall subcooling degree and increase in mass flux leads to the separation point at the neck of the injected flow moving towards the exit, while the annular flow region is expanding and the flow pattern transition is lagging. The mass flux improves the heat transfer coefficient more significantly at high vapor quality. During injection and bubble flow, the wall shear stress and local heat transfer coefficient are subject to bouncing and oscillations, which may induce fluctuations in the upstream annular flow. The prediction performance of six classical heat transfer correlations is evaluated. The results indicate that the Nie et al. correlation has the highest comprehensive prediction accuracy with MRD and MARD of -5.00 % and 15.83 %, respectively.

Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii-Moriya interaction

Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii-Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPT). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media

In this paper, we consider the time fractional thermoporoelasticity problem in fractured and heterogeneous media. The mathematical model with a time memory formalism is described by a coupled system of equations for pressure, temperature and displacements. We use an implicit finite difference approximation for temporal discretization. We present a fine grid approximation based on the finite element method and Discrete Fracture Model (DFM) for two-dimensional model problems. Further, we use the Generalized Multiscale Finite Element Method (GMsFEM) for coarse grid approximation. The primary concept behind the proposed method is to streamline the complexity inherent in the thermoporoelasticity problem. Given that our model equation incorporates multiple fractional powers, leading to multiple unknowns with memory effects, we aim to address this intricacy by optimizing the problem’s dimensionality. As a result, the solution is sought on a coarse grid, a strategic choice that not only simplifies the computational cost but also contributes to significant time savings. We present numerical results for the two-dimensional model problems in heterogeneous fractured porous media. We derive relative errors between the reference fine grid solution and the multiscale solution for different numbers of multiscale basis functions. The results confirm that the proposed method is able to achieve good accuracy with a few degrees of freedoms on the coarse grid.

The inclined conductive column effect: A new simple model for magnetotelluric anomalous phases

Summary Magnetotelluric data are sometimes accompanied by ‘anomalous’ impedance phases ($\phi $xy and $\phi $yx) in the off-diagonal components deviating from the first (0º < $\phi $xy < 90º) or third (−180º < $\phi $yx < −90º) quadrant, especially in long-period bands. This phenomenon is called the phases out-of-quadrant (POQ). The POQ poses a challenge in Magnetotelluric modeling because simple one- or two-dimensional models cannot explain it. Previous studies have reported that strong inhomogeneity, anisotropy, or particular three-dimensional structures, such as the L-shaped or cross-shaped conductors, could explain the POQ. Aside from these models, we have discovered that a slanted columnar conductor also generates the POQ. Our systematic investigation through the synthetic forward modeling of an inclined conductive column with a varying geometry showed that the inclination angle and the column length may affect the POQ appearance. We investigated herein the behavior of the electric currents around the inclined conductive column embedded in a resistive half space. We found that the induced electric field in the region with the POQ tends to point in the opposite direction to the surrounding vectors. This result can reasonably explain the inverted phase in long-period bands. Furthermore, we confirmed that current is sucked into one end of the column, but discharged from the other end, suggesting that the column works as a current channel. The localized reverse vectors are associated with the current channeling along the inclined conductor, which generates the POQ. A volcanic conduit within a resistive host rock is one of the typical field examples of such an inclined channel. Our study suggests that the POQ is a helpful clue in imaging the geometry of a volcanic magma plumbing system through Magnetotelluric surveys.

First-order formalism for β functions in bosonic sigma models from supersymmetry breaking

We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional “geometric” results obtained in the background field methods, in this way resolving the peculiarities pointed out in O. Gamayun [Peculiarities of beta functions in sigma models, ]. The result is achieved by the supersymmetric completion of the first-order sigma model. Published by the American Physical Society 2024

Error analysis for determining transverse tensile delamination strength of REBCO coated conductors by anvil test: numerical simulation demonstrations

Abstract RE-Ba-Cu-O (REBCO, where RE = Y, Gd, Sm, and other rare earth elements) coated conductor (CC) tapes exhibit considerable potential for application within the domains of high-energy physics and high-field science. Nevertheless, weak interfacial properties pose a significant obstacle, impeding the progress and practical implementation in high-field scenarios. The anvil tension method has been extensively employed for the assessment of transverse delamination strength of REBCO CC tapes. However, the outcomes derived from anvil tension exhibit severe dispersion, thereby impeding its efficacy in evaluating material performance. The underlying cause of this phenomenon remains unidentified. In this study, error analysis of anvil measurement method in determining the transverse tensile delamination strength (TTDS) of REBCO CC tapes was conducted based on finite element (FE) numerical simulations. A two-dimensional multilayer elastic-plastic delamination FE model with main layers of REBCO CC tapes, solder connecting layers and anvil materials were developed based on the bilinear cohesive zone model. The effects of anvil test conditions and the structural configuration of the conductor itself on the test results were discussed. Simulation results show that localized premature cracking of the interface due to stress concentration and plastic yielding of the CC tape around the loading boundary is the root reason for the discrepancy between the anvil test results and the true interfacial strength. Therefore, anvil test conditions (including top anvil dimensions, soldering conditions, loading eccentricity angle, and anvil material properties) as well as the structural configuration of the conductor itself (including edge initial crack length, edge encapsulation width, and stabilizer thickness) have a significant impact on anvil test-based TTDS results.

Two-dimensional models of core-collapse supernova explosions assisted by heavy sterile neutrinos

Two-dimensional models of core-collapse supernova explosions assisted by heavy sterile neutrinos

3D code for MAgneto-Thermal evolution in Isolated Neutron Stars, MATINS: thermal evolution and lightcurves

Abstract The thermal evolution of isolated neutron stars is a key element in unraveling their internal structure and composition and establishing evolutionary connections among different observational subclasses. Previous studies have predominantly focused on one-dimensional or axisymmetric two-dimensional models. In this study, we present the thermal evolution component of the novel three-dimensional magnetothermal code MATINS (MAgneto-Thermal evolution of Isolated Neutron Star). MATINS employs a finite volume scheme and integrates a realistic background structure, along with state-of-the-art microphysical calculations for the conductivities, neutrino emissivities, heat capacity, and superfluid gap models. This paper outlines the methodology employed to solve the thermal evolution equations in MATINS, along with the microphysical implementation which is essential for the thermal component. We test the accuracy of the code and present simulations with non-evolving magnetic fields of different configurations (all with electrical currents confined to the crust and a magnetic field that does not thread the core), to produce temperature maps of the neutron star surface. Additionally, for a specific magnetic field configuration, we show one fully coupled evolution of magnetic field and temperature. Subsequently, we use a ray-tracing code to link the neutron star surface temperature maps obtained by MATINS with the phase-resolved spectra and pulsed profiles that would be detected by distant observers. This study, together with our previous article focused on the magnetic formalism, presents in detail the most advanced evolutionary code for isolated neutron stars, with the aim of comparison with their timing properties, thermal luminosities and the associated X-ray light curves.

A case-history tutorial describing the incorporation of geophysical, petrophysical and geological constraints to generate realistic geological models of the Matheson Study Area, Ontario

The model that is used to explain potential-field data is highly dependent on the constraints applied in the modelling process. Many studies demonstrate the necessity of constraining gravity and magnetic models. However, typically they do not demonstrate the individual enhancements that come as a consequence of integrating each constraint into the geophysical model. In this paper, we show that when there are no constraints, it is possible to find an inverse model that is consistent with gravity data, but the model is unrealistic, as one sedimentary basin is too deep. Adding a depth weighting constraint can ensure the depth is correct, but all other features have the same depth, which is unrealistic. Including densities from a density compilation makes the densities at surface realistic, but the dips are all close to vertical and the thicknesses are similar, which is unrealistic. In this case, the inversion is believed to have found a local minimum close to the starting model. Reflection seismic data was used to constrain a two-dimensional (2D) modeling exercise (on multiple profiles) to determine the geometry of one sedimentary sub-basin. These 2D models were then combined to build a realistic three-dimensional (3D) starting model. An inversion from this model fixed the densities of each lithology, but allowed the thicknesses of the layers to vary. The resulting model was realistic, with the dips and thicknesses away from the seismic constraints being consistent with geological expectations. Although the fit to the data was much better than the previous model, it was poorer than hoped. If the densities were then allowed to vary within a realistic range of values, the fit could be improved so that both the fit to the data and the geologic model are realistic.

Modelling the effect of cell motility on mixing and invasion in epithelial monolayers.

Collective cell invasion underlies several biological processes such as wound healing, embryonic development, and cancerous invasion. Here, we investigate the impact of cell motility on invasion in epithelial monolayers and its coupling to cellular mechanical properties, such as cell-cell adhesion and cortex contractility. We develop a two-dimensional computational model for cells with active motility based on the cellular Potts model, which predicts that the cellular invasion speed is mainly determined by active cell motility and is independent of the biological and mechanical properties of the cells. We also find that, in general, motile cells out-compete and invade non-motile cells, however, this can be reversed by differential cell proliferation. Stable coexistence of motile and static cell types is also possible for certain parameter regimes.

Acoustic Sensors for Monitoring and Localizing Partial Discharge Signals in Oil-Immersed Transformers under Array Configuration

Partial discharge (PD) is one of the major causes of insulation accidents in oil-immersed transformers, generating a large number of signals that represent the health status of the transformer. In particular, acoustic signals can be detected by sensors to locate the source of the partial discharge. However, the array, type, and quantity of sensors play a crucial role in the research on the localization of partial discharge sources within transformers. Hence, this paper proposes a novel sensor array for the specific localization of PD sources using COMSOL Multiphysics software 6.1 to establish a three-dimensional model of the oil-immersed transformer and the different defect types of two-dimensional models. “Electric-force-acoustic” multiphysics field simulations were conducted to model ultrasonic signals of different types of PD by setting up detection points to collect acoustic signals at different types and temperatures instead of physical sensors. Subsequently, simulated waveforms and acoustic spatial distribution maps were acquired in the software. These simulation results were then combined with the time difference of arrival (TDOA) algorithm to solve a system of equations, ultimately yielding the position of the discharge source. Calculated positions were compared with the actual positions using an error iterative algorithm method, with an average spatial error about 1.3 cm, which falls within an acceptable range for fault diagnosis in transformers, validating the accuracy of the proposed method. Therefore, the presented sensor array and computational localization method offer a reliable theoretical basis for fault diagnosis techniques in transformers.

Transient thermal management of laser systems using Plate-Fin phase change heat Exchangers: Experimental and computational study

To mitigate transient thermal shocks in lasers and reduce thermal stresses caused by temperature fluctuations, the use of phase change materials (PCMs) in thermal management systems is a viable solution. This study proposes an innovative two-dimensional transient heat transfer model specifically designed for plate-fin phase change heat exchangers (PFPCHEs). The model meticulously simulates the complex heat transfer phenomena within the heat exchanger, including fluid convection, solid thermal conduction, and the phase change processes of PCM. The convective heat transfer coefficient between fluid and plate is calculated using the Wieting correlation. An advanced pulse-mode experimental test platform was constructed to validate the model, dynamically monitoring and recording outlet temperatures and heat exchange performance for stringent experimental comparison. The research explores the impact of key operating parameters such as initial temperature, flow rate, and inlet temperature of the cooling cycle on the performance of the heat exchanger, providing valuable design and control strategies for transient thermal management of laser systems. The experimental results confirm that the model accurately predicts the dynamic response characteristics and temperature distribution of PFPCHEs under multi-cycle pulse loads, with 96% of the predictions within a 10% error margin. A significant finding is that the initial temperature has negligible influence on the heat transfer characteristics when it is below the solid phase temperature of the PCM. Moreover, by meticulously adjusting the flow rate and inlet temperature of cooling cycle, it is possible to effectively maintain the stability of the outlet temperature throughout the entire pulse cycle. This is crucial for minimizing temperature fluctuations within the thermal management system and extending the service life of electronic components.

Debonding inspection with an enhanced miniature EMAT based on multiple pulse echoes

The present paper proposes a non-contact ultrasonic testing method for the debonding inspection of metal-based composite structures, utilizing an improved electromagnetic acoustic transducer (EMAT). The enhanced EMAT incorporates a carbonyl iron powder coil backplate and a small butterfly coil to enhance the detecting ability for interfacial bonding. A two-dimensional finite element model is developed to quantify the effectiveness of the carbonyl iron powder coil backplate on increasing the eddy current density and the magnetic flux density in the specimen. An experimental setup was designed using the Ritec SNAP 5000 and the improved EMATs to examine an aluminium-epoxy resin composite structure. Ultrasonic C-scan images of the specimen's bonding interface were obtained from the experiment. Both simulation and experimental results show that carbonyl iron powder coil backplates can increase the efficiency of the EMATs. By investigating the influence of echo number on debonding detection, it was revealed that employing higher-order echoes and utilizing carbonyl iron powder as the coil backplate can enhance the debonding detection capability. The C-scan imaging results indicate that the utilization of high-order echoes enhances imaging quality, and the employment of high-quality miniaturized EMATs enhances the capability for quantitative analysis of debonding defects.

Orientation-position coupling in the two-dimensional XY model

Orientation-position coupling in the two-dimensional XY model

Two-Dimensional Hydrodynamic Simulation of the Effect of Stormwater Inlet Blockage on Urban Waterlogging

The drainage capacity of stormwater inlets, which serve as the connection between the surface and the underground drainage system, directly affects surface runoff and the drainage capacity of underground drainage systems. However, in reality, stormwater inlets are often blocked due to the accumulation of leaves, human waste disposal and other factors, resulting in a greatly reduced drainage capacity of the drainage network and, in turn, urban waterlogging disasters. In view of the problem of stormwater inlet blockage, employing a typical waterlogging point in the Lianjiang Middle Road area of Fuzhou city as the research object, the stormwater inlet equivalent drainage method was adopted in this paper to characterize the drainage capacity of the pipe network and enable the control of the stormwater inlet blockage state. Coupled with the stormwater inlet drainage equation, an improved ITF-FLOOD two-dimensional hydrodynamic model was constructed, and the influence of stormwater inlet blockage on urban waterlogging under different rainfall return periods was simulated and analyzed. With increasing rainfall return period, the influences of stormwater inlet blockage on both the maximum area and the depth of accumulated water in the study area gradually decreased compared with those of a nonblocked stormwater inlet, and the growth proportions decreased from 43.35% and 34.58% under the 1-year rainfall scenario to 3.34% and 9.76% under the 50-year rainfall scenario, respectively. However, in terms of the change in the accumulated water level, stormwater inlet blockage will cause an increase, and the influence will always be significant. Overall, stormwater inlet blockage aggravated the waterlogging risk and the extent of waterlogging. Therefore, the results provided a reference for the construction of an urban waterlogging model and have certain guiding significance for waterlogging prevention and control in the study area prone to stormwater inlet blockage.

Numerical investigations of GRS wall performance with tiered configurations

Geosynthetic Reinforced Soil (GRS) walls have become increasingly popular as a result of their numerous advantages. In some cases these structures are constructed in a multi-tiered configuration, which makes their behavior more complicated. Nevertheless, the response of the multi-tiered walls is insufficiently explained by the existing design manuals and literature studies. This paper investigated the performance of GRS walls with multi-tiered configurations using two-dimensional (2D) finite element numerical models. This study compares the performance of two-tiered GRS walls with simple GRS walls (single-tiered). It also examines the impact of offset distance, backfill strength properties, and reinforcement parameters (vertical spacing and reinforcement length) on horizontal deformations and reinforcement tensile loads in two-tiered GRS walls. Adopting a multi-tiered configuration for GRS walls can significantly reduce both the horizontal wall deformation and the maximum reinforcement tensile loads. Additionally, the critical offset distance found in this study is significantly smaller than that recommended by the Federal Highway Administration (FHWA) guidelines. The finite element results also demonstrate that using high-quality backfill soil can minimize interaction between lower and upper tiers. Using a uniform reinforcement length of 0.6H for both tiers significantly reduces horizontal deformation compared to the FHWA recommendation of 0.6H and 0.35H for the lower and the upper tier respectively.

Simulation and Experimental Investigation of the Effect of Pore Shape on Heat Transfer Behavior of Phase Change Materials in Porous Metal Structures

With the gradual increase in energy demand in global industrialization, the energy crisis has become an urgent problem. Due to high heat storage density, small volume change, and nearly constant transition temperature, phase change materials (PCMs) provide a promising method to store thermal energy. In this work, we designed and fabricated three kinds of porous metal structures with hexagonal, rectangular, and circular pores and explored the phase change process of PCMs within them. A two-dimensional numerical model was established to investigate the heat transfer process of PCMs within different shapes of porous metal structures and analyze the influence of heat source location on the thermal performance of the thermal storage units. Visualization experiments were also carried out to reveal the melting process of PCMs within different porous metal structures by a digital camera. The results show that paraffin in a porous metal structure with hexagonal pores has the fastest melting rate, while that in a porous metal structure with circular pores has the slowest melting rate. Under the bottom heating mode, the melting time of the paraffin in porous metal structures with hexagonal pores is shortened by 18.6% compared to that in porous metal structures with circular pores. Under the left heating mode, the corresponding melting time is shortened by 16.7%. These findings in this work will offer an effective method to design and optimize the structure of porous metal and improve the thermal properties of PCMs.

Selective anticancer effects of plasma-activated saline in 3D tumor model co-culturing of normal cells and cancer cells

Compared with conventional two-dimensional (2D) cell culture model, the 3D tumor model constructed in vitro is better representative of the tumor microenvironment in vivo. Here, we proposed the utilization of 3D tumor model of co-cultured cancer cells and normal cells to evaluate the selective anticancer effects of cold atmospheric plasma-activated saline (PAS), and expected to provide more precise information about PAS-tumor interactions. By cell sorting, we clarified that A375 melanoma cells and HaCaT normal skin cells purified from the 3D multicellular tumor model differ in sensitivity and responsiveness to PAS compared to the 2D culture model. And during the optimization of PAS treatment parameters, we further found that A375 cells were almost completely killed while HaCaT cells were still present in large numbers after 5 d of certain PAS treatment. Our experiment innovatively carries out the selective study of plasma technology in 3D co-culture system and provides a theoretical basis for further clinical and practical applications of PAS.