One-dimensional Model Research Articles

High Current Density Operation of a Proton Exchange Membrane Fuel Cell with Varying Inlet Relative Humidity—A Modeling Study

This paper focuses on proton exchange membrane fuel cell (PEMFC) operation at current densities in the order of 6 A/cm2. Such high current densities are conceivable when the traditional carbon fiber papers are replaced with perforated metal plates as the gas diffusion layer to enhance waste heat removal, and at the same time the relative humidity inside the fuel cell is kept below 100% by applying appropriate operating conditions as was found in previous one-dimensional modeling work. In the current paper, we applied a three-dimensional, multi-phase computational fluid dynamics model based on Ansys-CFX to obtain additional insight into the underlying physics. The calculated pressure drops are in very good agreement with previous one-dimensional modeling work, and the current densities in all case studies are in the order of 5–6 A/cm2, but different from the previous one-dimensional study, the results suggest that the relative humidity is very close to 100% throughout the entire channel length when the inlet relative humidity is 100%, ensuring best hydration cell conditions and hence best performance. Importantly, the model results suggest that fuel cell performance at a high current density in conjunction with relatively low stoichiometric flow ratios around 1.5–2 is possible.

A Deep Learning Estimation for Probing Depth of Transient Electromagnetic Observation

The probing depth of the transient electromagnetic method (TEM) refers to the depth range at which the underground conductivity changes can be effectively detected. It typically ranges from tens of meters to several kilometers and is influenced by factors such as instrument parameters and the conductivity of the subsurface structure. Rapid and accurate probing depth is useful for the selection of appropriate inversion parameters and improving survey accuracy. However, mainstream methods suffer from issues such as low computational precision, large uncertainties, or high computational requirements, making them unsuitable for processing massive airborne electromagnetic data. In this study, we propose a prediction model based on deep learning that can directly compute the probing depth from the TEM responses, and its effectiveness and accuracy are validated through synthetic models and field measurements. We compared the performance of classic deep learning models, including CNN, RESNET, and RNN, and found that RNN performed the best overall on both synthetic and field data. Furthermore, we apply this algorithm to deep learning-based ATEM inversion by constraining the one-dimensional resistivity model depths in the training set, to reduce the non-uniqueness of the inversion, accelerate the convergence, and improve its prediction accuracy.

Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes

We investigate the observables of the one-dimensional model for anomalous transport in semiconductor devices where diffusion arises from scattering at dislocations at fixed random positions, known as the Lévy-Lorentz gas. To gain insight into the microscopic properties of such a stochastically complex system, deterministic dynamics known as the slicer map and fly-and-die dynamics are used. We analytically derive the generalized position autocorrelation function of these dynamics and study the special case, the 3-point position correlation function. For this, we derive single-parameter-dependent scaling and compare it with the numerically estimated 3-point position autocorrelation of the Lévy-Lorentz gas, for which the analytical expression is still an open question. Here we obtained a remarkable agreement between them, irrespective of any functional relationship with time. Moreover, we demonstrate that the position moments and the position autocorrelations of these systems scale in the same fashion, provided the times are large enough and far enough apart. Other observables, such as velocity moments and correlations, are reported to distinguish the systems. Published by the American Physical Society 2024

One-dimensional Dexter-type excitonic topological phase transition

The concept of the Su-Schrieffer-Heeger model, which was successfully introduced in topological photonics, can also be applied to the study of topological excitonics. Here we study the topological properties of a one-dimensional excitonic tight-binding model formed by two-level systems by taking into account the charge transfer and local excitations. The interactions between the two types of excitons give rise to a rich spectrum of physics, including the nontrivial topological phase in the uniform chain, unlike the conventional Su-Schrieffer-Heeger model, the topologically nontrivial flat bands, and, most importantly, the excitonic topological phase transition assisted by the Dexter electron exchange process. The excitonic topological phase leads to the development of “chiral superposition.” The topological edge states are robust because they are protected by the inversion symmetry. Based on our calculations, experiments for observing the edge states optically in a molecular chain are proposed. Published by the American Physical Society 2024

A local enhanced mamba network for hyperspectral image classification

Deep learning has significantly advanced hyperspectral image (HSI) classification, primarily due to its robust nonlinear feature extraction capabilities. The vision transformer has achieved notable performance but is limited by the quadratic computational burden of its self-attention mechanism. Recently, a network based on state space model named Mamba, has attracted considerable attention for its linear complexity and commendable performance. Nevertheless, Mamba was originally designed for one-dimensional causal sequence modeling, and its effectiveness in inherent non-causal HSI classification remains to be fully validated. To address this issue, we propose a novel Local Enhanced Mamba (LE-Mamba) network for hyperspectral image classification, which mainly comprises a Local Enhanced Spatial SSM (LES-S6), a Central Region Spectral SSM (CRS-S6), and a Multi-Scale Convolutional Gated Unit (MSCGU). The LES-S6 improves non-causal local feature extraction by incorporating a multi-directional local spatial scanning mechanism. Additionally, the CRS-S6 employs a bidirectional scanning mechanism in the spectral dimension to capture fine spectral details and integrate them with spatial information. The MSCGU utilizes a convolutional gating mechanism to aggregate features from diverse scanning routes and extract high-level semantic information. The overall accuracies of LE-Mamba on Indian Pines, WHU-Hi-HanChuan, WHU-Hi-LongKou, and Pavia University datasets are 99.16 %, 98.16 %, 99.57 %, and 99.63 %, respectively. Extensive experimental results on these four public datasets demonstrate that the LE-Mamba outperforms eight mainstream deep learning models in classification performance.

Thermodynamic analysis and equilibration response time prediction of recuperator in the SCO2 Brayton cycle

The recuperator of supercritical carbon dioxide (SCO2) Brayton cycle significantly affects the system's flexible control due to its thermal inertia. In this study, the structural parameters and operating parameters of recuperator are considered to quantitatively analyze the law of their influence on equilibration response time. Chebyshev spectrum method has been innovatively applied to the one-dimensional dynamic response model of recuperator. The dynamic response time of recuperator under the condition of temperature variation on the hot side is analyzed. The results show that reducing the thermal inertia of solid wall (by increasing the specific surface area of recuperator) can effectively decrease the equilibrium time. Additionally, the rate of inlet temperature variation should not be too large to reduce the thermal inertia of fluid. The zigzag channel demonstrates better dynamic response characteristic than straight channel. A novel dimensionless formula, based on structure and operating parameters, is proposed to quantitatively characterize and predict the equilibrium time for both straight and zigzag channel, the error is within ±20 %. Moreover, a high-precision neural network is trained to predict the equilibrium time directly. The results provide significant theoretical and application support for alleviating the thermal inertia of PCHE and improving the flexibility of SCO2 system.

Diameters of Symmetric and Lifted Simple Exclusion Models

We determine diameters of Markov chains describing one-dimensional N-particle models with an exclusion interaction, namely the symmetric simple exclusion process (Ssep) and one of its non-reversible liftings, the lifted totally asymmetric simple exclusion process (Tasep). The diameters provide lower bounds for the mixing times, and we discuss the implications of our findings for the analysis of these models.

Electrochemical and aging model of li-ion batteries and estimation of total number of cycles during the lifecycle of the battery

Fast charging is a critical factor for the widespread adoption of electric vehicles (EVs), yet it poses challenges to the durability of lithium-ion batteries (LiBs). This study develops an aging model for a 10 Ah LiB cell using COMSOL Multiphysics, integrating a one-dimensional electrochemical model with a zero-dimensional thermal model. The model is constructed using cell design and electrochemical parameters derived from existing literature, tailored to the specific electrode and electrolyte materials utilized in this study. Key aging phenomena, such as the Solid Electrolyte Interface (SEI) growth and lithium plating, are embedded within the model to simulate the aging patterns and the interplay between these factors across various C-rates and temperatures. Simulation results suggest that while higher charging rates can reduce charging time, they also lead to increased degradation, with lithium plating becoming more severe at these elevated rates. The model also indicates that temperature management during cell operation can influence cycle life, with strategic temperature increases potentially mitigating some negative effects of fast charging. The study also explores the concept of total charging time as an alternative metric for battery wear, examining its relationship with the charging current profile and temperature. Results indicate that while fast charging offers convenience, it significantly impacts cycle life, underscoring the need for optimized charging strategies. The insights from this work enhance the understanding of Li-ion cell aging mechanisms, shedding light on the complex trade-offs between charging speed, temperature management, and lifespan. This contributes to the development of more sophisticated battery management systems and charging protocols that aim to extend the operational life of LiBs while accommodating the demands of fast charging.

A study of the spatial non-uniformity of reverberation time at low frequencies

This paper presents a study of the spatial non-uniformity of low-frequency reverberation time estimates. Using measured and simulated data, it is demonstrated that the reverberation times estimated from band-limited impulse responses vary as a function of space at low frequencies. The origin of this spatial dependency is investigated using a one-dimensional finite element model. It is shown that the Q-factor and reverberation time at the resonant frequency of a particular mode are spatially dependent and that the spatial dependency is related to the mode shapes. The ranges of the reverberation time estimates as a function of third-octave frequency bands in simulated and measured rooms are presented. An additional finding is that modal damping constants (obtained via eigenvalue analysis) quantify the decay of uncoupled modes but not necessarily the reverberation time. These observations have implications for measurements and simulations of reverberation time at low frequencies. When measuring a spatially averaged reverberation time, the choice of source and receiver positions is important. A guideline is proposed that defines a set of preferred measurement positions based on the mode shapes, from which estimates of the spatially averaged reverberation time can be obtained.

ANATOMICAL VARIATIONS IN A FINITE ELEMENT NERVE MODEL OF THE HUMAN FOOT

The nerves in the foot offer a significant role in controlling the movement and correct loading of the foot by providing continuous feedback to the central nervous system. The health importance in the anatomical variations of nerves, such as the locations, the lengths, the communicating branches, and the distance between the adjacent nerve terminals between individuals have given prominence to anatomists as well as physiologists. A previously developed one-dimensional (1D) model of the nerve was extended to determine different anatomical variations in the nerves of the foot, as a realistic anatomical-based variant nerve model of the human foot is not available. The model was verified against experimental data from the literature for communicating branches and distances of various area of the human foot. For instance, the simulated distances of the communicating branches of the plantar nerves and medial dorsal cutaneous nerve (MDCN) division proximal to the first digital space were found to be 43.3 mm and 112.3 mm, respectively, which was in general agreement with the experimental distances of 8-56 mm and 96-116.74 mm, respectively. The developed nerve variant model provides a platform for future studies of the various geometrical and efficient concerns of neurovascular diseases such as diabetic neuropathies by determining the parameters of nerve conduction studies.

Addressing Mass Conservation in Two-Dimensional Modeling of Lithium Metal Batteries with Electrochemically Plated/Stripped Interfaces

Several previous studies have aimed to develop mathematical models based on the moving boundary approach for predicting changes in lithium morphology during the cycling of lithium metal batteries under different operating conditions. These modeling frameworks play a crucial role in enhancing our fundamental understanding of the transport and reaction mechanisms and guide experimentalists in developing safer and more efficient lithium metal anodes. In this work, using a simple two-dimensional model for the lithium metal battery, we aim to bring attention to the bulk convection in the liquid electrolytes induced by the movement of the lithium metal surface modeled as a moving boundary. The back-and-forth motion of the lithium metal surface during the plating and stripping of lithium introduces a weak fluid motion in the liquid electrolyte that should be incorporated in the model equations and corresponding boundary conditions (Figure 1). The results for the electrochemical signatures and morphology evolution thus obtained by solving a coupled fluid model are compared with the case where the velocity distribution in the liquid electrolyte is ignored. This work extends our previously reported perspective on the convective flux correction to rectify the mass conservation failures at moving boundaries in one-dimensional models to two dimensions. This careful implementation of the correct boundary conditions ensures the mass conservation of lithium in two-dimensional simulations for predicting the morphological evolution of lithium metal electrodes over cycles. These revised battery models with accurate mass and charge conservation are crucial for predicting the performance of the battery over cycles. Additionally, these relative fluxes at the moving and fixed boundaries are sometimes ignored by assuming a bulk concentration condition at the far end, especially at the cathode/separator interface. While it may not affect overpotential signatures at the anode, it leads to mass conservation issues with implications for the accuracy of cycling simulations. Thus, with the help of a two-dimensional electro-convection model, this study addresses the role of bulk convection in liquid electrolytes and the importance of ensuring mass conservation in lithium metal battery models.

Transport Effects in Electrochemical Biochip Sensors with Redox Cycling Amplification: Computational and Experimental Analysis

In the last few decades, and especially after the COVID-19 pandemic, point-of-care diagnostics and field-deployable biosensors have attracted significant attention. Key components of these instruments are microchips that integrate microfluidics with a sensor (e.g., optical or electrochemical) to provide rapid, low-cost, real-time detection of analyte molecules in very small volumes. Next-generation electrochemical sensors have been miniaturized on solid-state platforms (e.g., arrays and vectors) where the area is limited. However, as the active surface area of the sensors decreases from a few square microns to sub-micron and nanometric scales, the measured currents drop, hence affecting the limit of detection. As the concentration of many analytes in the physiological environment is low, low signal-to-noise ratios have limited the miniaturization of standard electrochemical sensors. One way to increase signal at the sensor output is by redox amplification. To achieve amplification, a second working electrode must be incorporated close to the first working electrode and proper bias must be applied to both. Micrometer-sized interdigitated electrode arrays have been fabricated using robust and scalable processes based on optical lithography and reactive ion-etching techniques. In some cases, IDAs have been integrated into microfluidics devices. The physical and electrochemical phenomena that occur in microfluidic channels under flow have been previously evaluated and showed an increase of current under flow. The effect of redox cycling in microfluidic and nanofluidic systems has also been qualitatively demonstrated. Some studies measured the amplification in the cases with and without flow and showed that the flow itself amplifies the measured electrochemical current, though in most cases, it reduces the amplification factor.Towards a more quantitative investigation, analytical and computational modeling were used, providing meaningful insights into the physics of IDAs without requiring numerous device fabrications. In this work, we used COMSOL Multiphysics to create a full three-dimensional simulation-based model of a real device in order to study the effect of laminar flow on redox cycling, as well as a simplified one-dimensional model for the analysis of transition velocity between different amplification regimes. IDAs with 5-10 mm for both electrodes width and gap were studied numerically and experimentally. The results of the 3D and 1D simulations were consistent between themselves, and also with those of the physical experiments. The relationship between the two mass transfer methods — diffusion and convection — were analyzed at different flow velocities and for different electrode geometries.Here we report a study of transport effects on a microfluidic sensor-chip in which electrochemical sensing is amplified by redox cycling using an interdigitated electrode array (IDA). Our models indicate that there exist two dominant regimes: one which is limited by redox cycling diffusion—a unique feature of IDAs— which is dominant at relatively low flow rates, and another which is limited by convection and has dominant flow effects which are effective at high flow rates (see Figure). The transition velocity between the two sensing regimes depends on the width of the electrode and spacing. It was found to be Vflow [mm/sec]=0.335/L[μm] + 0.04 which is similar to the prediction of Vflow∝1/L obtained from the one-dimensional model.An understanding of the combined effects of redox cycling and convection flow is critical as microfluidic chips with electrochemical sensing amplified by redox cycling using IDAs are becoming widely used in diagnostic assays. The method for prediction of current under any flow rate described here will support technological development of more efficient and accurate devices. Figure 1

Origins of fine structure in DNA melting curves.

With the help of the one-dimensional random Potts-like model, we study the origins of fine structures observed on differential melting profiles of double-stranded DNA. We theoretically assess the effects of sequence arrangement on DNA melting curves through the comparison of results for random, correlated, and block sequences. Our results re-confirm the smearing out of the fine structure with the increase in chain length for all types of sequence arrangements and suggest that the fine structure is a finite-size effect. We have found that the fine structures on melting curves of chains comprised of blocks with correlations in sequence are more persistent, probably because of increased sequence disorder the blocks introduce. Many natural DNAs show a well-expressed fine structure of melting profiles. Our results for block sequences may suggest the existence of such sequence motifs in natural DNA sequences.

Deep neural networks as variational solutions for correlated open quantum systems

In this work we apply deep neural networks to find the non-equilibrium steady state solution to correlated open quantum many-body systems. Motivated by the ongoing search to find more powerful representations of (mixed) quantum states, we design a simple prototypical convolutional neural network and show that parametrizing the density matrix directly with more powerful models can yield better variational ansatz functions and improve upon results reached by neural density operator based on the restricted Boltzmann machine. Hereby we give up the explicit restriction to positive semi-definite density matrices. However, this is fulfilled again to good approximation by optimizing the parameters. The great advantage of this approach is that it opens up the possibility of exploring more complex network architectures that can be tailored to specific physical properties. We show how translation invariance can be enforced effortlessly and reach better results with fewer parameters. We present results for the dissipative one-dimensional transverse-field Ising model and a two-dimensional dissipative Heisenberg model compared to exact values.

Dynamic behaviour and energy dissipation of offline air pockets in transient pipe flows

ABSTRACT The traditional one-dimensional (1D) model often fails to accurately predict the dynamic pressure response of large offline air pockets during transients, due to a lack of comprehensive understanding of the underlying mechanisms of transient interaction with offline air pockets. This study investigated dynamic behavior and energy dissipation of offline air pockets through experiments and numerical models. Experimental pressure responses were predicted using a 1D-3D coupling model, which presented superior performance compared to traditional 1D model. The 1D-3D coupling model was further utilized to investigate the air-water interface, internal energy and turbulence distribution of offline air pockets. The results reveal that the stability of the air-water interface depends on the decelerating distance of the jet in offline tube, explaining the instability phenomenon with lower water levels observed in experimental snapshots. The internal energy pattern suggests different energy dissipation mechanisms compared to the inline air pockets. The distribution of turbulence intensity and effective thermal conductivity indicates significant additional energy dissipation at the inlet and outlet of offline neck. By incorporating a minor head loss term for offline neck into traditional 1D model, the pressure response aligns well with the results obtained from 1D-3D coupling model under different flow rates and air volumes.

Numerical signatures of ultra-local criticality in a one dimensional Kondo lattice model

Heavy fermion criticality has been a long-standing problem in condensed matter physics. Here we study a one-dimensional Kondo lattice model through numerical simulation and observe signatures of local criticality. We vary the Kondo coupling J_KJK at fixed doping x. At large positive J_KJK, we confirm the expected conventional Luttinger liquid phase with 2k_F=\frac{1+x}{2}2kF=1+x2 (in units of 2\pi2π), an analogue of the heavy Fermi liquid (HFL) in the higher dimension. In the J_K ≤ 0JK≤0 side, our simulation finds the existence of a fractional Luttinger liquid (LL\star⋆) phase with 2k_F=\frac{x}{2}2kF=x2, accompanied by a gapless spin mode originating from localized spin moments, which serves as an analogue of the fractional Fermi liquid (FL\star⋆) phase in higher dimensions. The LL\star⋆ phase becomes unstable and transitions to a spin-gapped Luther-Emery (LE) liquid phase at small positive J_KJK. Then we mainly focus on the “critical regime” between the LE phase and the LL phase. Approaching the critical point from the spin-gapped LE phase, we often find that the spin gap vanishes continuously, while the spin-spin correlation length in real space stays finite and small. For a certain range of doping, in a point (or narrow region) of J_KJK, the dynamical spin structure factor obtained through the time-evolving block decimation (TEBD) simulation shows dispersion-less spin fluctuations in a finite range of momentum space above a small energy scale (around 0.035 J0.035J) that is limited by the TEBD accuracy. All of these results are unexpected for a regular gapless phase (or critical point) described by conformal field theory (CFT). Instead, they are more consistent with exotic ultra-local criticality with an infinite dynamical exponent z=+z=+. The numerical discovery here may have important implications on our general theoretical understanding of the strange metals in heavy fermion systems. Lastly, we propose to simulate the model in a bilayer optical lattice with a potential difference.

Large deviations in the symmetric simple exclusion process with slow boundaries: A hydrodynamic perspective

We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have been recently derived using exact microscopic analysis by Derrida, Hirschberg and Sadhu in [J. Stat. Phys. 182, 15 (2021)]. We present an independent derivation using the hydrodynamic approach of the macroscopic fluctuation theory (MFT). The slow coupling introduces additional boundary terms in the MFT-Action, which modifies the spatial boundary conditions for the associated variational problem. For the density large deviations, we explicitly solve the corresponding Euler-Lagrange equations using a simple local transformation of the optimal fields. For the current large deviations, our solution is obtained using the additivity principle. In addition to recovering the expression of the large deviations functions, our solution describes the most probable path for these rare fluctuations.

Numerical simulation of one-dimensional perovskite solar cell model

Perovskite solar cell (PSC) is one of the advanced third-generation solar cells that have rapid efficiencies but instability issues in terms of air, moisture, and UV light sensitivity becomes a barrier to commercialization. The instability issue is due to the charge accumulation at the interface of the PSC reducing its efficiency. This research focuses on the operation of PSCs through a one-dimensional (1D) drift-diffusion model for planar heterojunction PSCs. The model also accounts for the electric potential by Poisson’s equation, the ion generation, and the recombination rate. The method of lines technique is applied to solve the model for the perovskite layer numerically using the finite difference method which is then solved forward in time using the ‘ode15s’ solver in MATLAB. It is highlighted that the comparison with the experimental data from the reference shows good agreement. The effect of parameter thickness variation of the perovskite layer upon the efficiency of PSCs is analyzed. The result shows that the best efficiency obtained is 19.77% obtained at thickness 0.25 𝜇𝑚. The results may prove useful for a guideline of the cell thickness that predicts the perovskites cell performance.

Nondetections of Helium in the Young Sub-Jovian Planets K2-100b, HD 63433b, and V1298 Tau c

We search for excess in-transit absorption of neutral helium at 1.083 μm in the atmospheres of the young (<800 Myr) sub-Jovian (0.2–0.5 RJ ) planets HD 63433b, K2-100b, and V1298 Tau c using high-resolution (R∼25,000) transit observations taken with Keck II/NIRSPEC. Our observations do not show evidence of helium absorption for any of the planets in our sample. We calculate 3σ upper limits on the planets’ excess helium absorption of <0.47% for HD 63433b, <0.56% for K2-100b, and <1.13% for V1298 Tau c. In terms of equivalent width, we constrain these to <2.52, <4.44, and <8.49 mÅ for HD 63433b, K2-100b, and V1298 Tau c, respectively. We fit our transmission spectra with one-dimensional Parker wind models to determine upper limits on the planets’ mass-loss rates of <7.9 × 1010, <1.25 × 1011, and <7.9 × 1011g s−1. Our nondetections align with expectations from one-dimensional hydrodynamic escape models, magnetic fields, and stellar wind confinement. The upper limits we measure for these planets are consistent with predicted trends in system age and He equivalent width from 1D hydrodynamic models.

Fast time-domain solution of the cochlear transmission line model in real-time applications.

A fast numerical time-domain solution for a one-dimensional cochlear transmission-line model was proposed for real-time applications. In this approach, the three-dimensional solver developed by Murakami [J. Acoust. Soc. Am. 150(4), 2589-2599 (2021)] was modified to develop a solution for the one-dimensional model. This development allows the solution to accurately and quickly calculate cochlear responses. The present solution can solve the model in real-time under coarse grid conditions. However, under fine-grid conditions, the computation time is significantly longer than the duration of the signal. Nevertheless, calculations can be performed under the fine grid condition, which previously required much computation time. This fact is essential to applications.