One-dimensional Model Research Articles

Modelling spatio-temporal interactions between second messengers Ca and cAMP in a pancreatic -cell.

Calcium serves as a widespread second messenger in almost every human and animal cell. The regulation of various cellular processes, such as transcriptional control and the kinetics of membrane channels, is significantly influenced by intracellular calcium ions (Ca ), and linkages between Ca and other second messengers should activate signaling networks. The passage of ions across the cell membrane regulates Ca levels in pancreatic -cells and requires the coordinated interaction of various ion transport mechanisms and organelles. The signaling of Ca in -cells and its interactions with the intracellular dynamics of cyclic adenosine monophosphate (cAMP) is poorly understood. Therefore, the current investigation proposes a mathematical model to illustrate the spatiotemporal dynamical interaction between Ca and cAMP. In order to construct a one-dimensional mathematical model, the fundamental initial and boundary conditions derived from the physiological characteristics of the -cell are incorporated. The numerical results were obtained by MATLAB simulations using the finite element method and the Crank-Nicolson method. The current study aims to offer an update on regulation between Ca and cAMP signaling circuits, with a focus on interactions that occur in localized areas of the -cell. The model gives the individual effect of each parameter on the regulation of Ca and cAMP profiles in a -cell. Evidently, impairments in the regulation of messenger pathways contribute to the pathological conditions, as demonstrated by the results obtained.

Kinetics of the one-dimensional voter model with long-range interactions

Abstract The voter model is an extremely simple yet nontrivial prototypical model of ordering dynamics, which has been studied in great detail. Recently, a great deal of activity has focused on long-range statistical physics models, where interactions take place among faraway sites, with a probability slowly decaying with distance. In this paper, we study analytically the one-dimensional long-range voter model, where an agent takes the opinion of another at distance r with probability ∝ r−α. The model displays rich and diverse features as α is changed. For α > 3 the behavior is similar to the one of the nearest-neighbor version, with the formation of ordered domains whose typical size grows as R(t) ∝ t1/2 until consensus (a fully ordered configuration) is reached. The correlation function C(r,t) between two agents at distance r obeys dynamical scaling with sizeable corrections at large distances r > r∗(t), slowly fading away in time. For 2 < α ≤ 3 violations of scaling appear, due to the simultaneous presence of two lengh-scales, the size of domains growing as t(α−2)/(α−1), and the distance L(t) ∝ t1/(α−1) over which correlations extend. For α ≤ 2 the system reaches a partially ordered stationary state, characterised by an algebraic correlator, whose lifetime diverges in the thermodynamic limit of infinitely many agents, so that consensus is not reached. For a finite system escape towards the fully ordered configuration is finally promoted by development of large distance correlations. In a system of N sites, global consensus is achieved after a time T ∝ N2 for α>3,T ∝Nα−1 for2<α≤3,andT ∝N forα≤2.

Limitations of mean-field approximations in describing shift-current and injection-current in materials

We theoretically and computationally investigate bulk photovoltaic effects, with a specific focus on shift-current and injection-current. Initially, we perform a numerical analysis of the direct current (dc) induced by a laser pulse with a one-dimensional model, utilizing mean-field theories such as time-dependent Hartree–Fock and time-dependent Hartree methods. Our numerical results, obtained with mean-field theories, reveal that the dc component of the current, as a second-order nonlinear effect, exists even after irradiation with linearly polarized light as a second-order nonlinear effect, indicating the generation of injection-current. Conversely, when we employ the independent-particle approximation, no injection-current is generated by linearly polarized light. To develop the microscopic understanding of injection-current within the mean-field approximation, we further analyze the dc component of the current with the perturbation theory, employing the mean-field approximations, the independent-particle approximation, and the exact solution of the many-body Schrödinger equation. The perturbation analysis clarifies that the injection-current induced by linearly polarized light under the mean-field approximations is an artifact caused by population imbalance, created through quantum interference from unphysical self-excitation pathways. Therefore, investigation of many-body effects on the bulk photovoltaic effects have to be carefully conducted in mean-field schemes due to potential contamination by unphysical dc current. Additionally, we perform the first-principles electron dynamics calculation for BaTiO3 based on the time-dependent density functional theory, and we confirm that the above findings from the one-dimensional model calculation and the perturbation analysis apply to realistic systems. Published by the American Physical Society 2024

An Improved Positive Displacement Pump Model Accounting for Suction Cavitation

Abstract Positive displacement (PD) pumps are widely employed in industrial settings due to their inherent simplicity and reliability, serving a diverse range of applications from slurry transport to jet washing. Although their operational principles are straightforward, the fluid dynamics of the pumped medium exhibit non-trivial characteristics, including intricate transient phenomena. Consequently, a comprehensive fluid dynamic description, such as a three-dimensional RANS analysis, presents challenges due to its demanding computational requirements. While simpler analytical PD pump models are available, they often fail to adequately represent the primary system behaviors, particularly when dealing with cavitation. Motivated by these challenges, this study aims to develop a novel one-dimensional model for PD pumps, offering a representation of essential fluid phenomena without imposing significant computational burdens. After assessing the relative importance of the fluid dynamic behaviors that the model must capture, we construct a pump model based on a one-dimensional fluid description and solve it using a second-order in time and space MUSCL-TVD scheme. The model's validity is confirmed by its application to both single-chamber and three-chamber diaphragm PD pumps, which are instrumented for experimental validation. The results of the one-dimensional model exhibit strong agreement with physical experiments, both in controlled laboratory environments and field conditions. This success suggests a promising approach for industrial applications.

Non-coplanar helimagnetism in the layered van-der-Waals metal DyTe3

Van-der-Waals magnetic materials can be exfoliated to realize ultrathin sheets or interfaces with highly controllable optical or spintronics responses. In majority, these are collinear ferro-, ferri-, or antiferromagnets, with a particular scarcity of lattice-incommensurate helimagnets of defined left- or right-handed rotation sense, or helicity. Here, we report polarized neutron scattering experiments on DyTe3, whose layered structure has highly metallic tellurium layers separated by double-slabs of dysprosium square nets. We reveal cycloidal (conical) magnetic textures, with coupled commensurate and incommensurate order parameters, and probe the evolution of this ground state in a magnetic field. The observations are well explained by a one-dimensional spin model, with an off-diagonal on-site term that is spatially modulated by DyTe3’s unconventional charge density wave (CDW) order. The CDW-driven term couples to antiferromagnetism, or to the net magnetization in an applied magnetic field, and creates a complex magnetic phase diagram indicative of competing interactions in this easily cleavable van-der-Waals helimagnet.

Numerical investigation of roping in multi-die meltblowing

This work aims at conducting a numerical investigation of the effect of the inter-die distance on the probability of roping during meltblowing. The results are qualitatively compared with the experimental data obtained by the present group in studies of roping in a model situation of solution blowing. The effectiveness of nonwoven products as filter membranes and others depends on the fiber size and geometrical fiber distributions in fiber mats. Jet roping in meltblowing results in a distortion of the laydown structure, which is detrimental to the product's efficiency. A quasi one-dimensional model is utilized here to predict the probability of jet–jet intersection in flight leading to roping, which was observed experimentally in the prior works of this group. The results of the present work are expected to be helpful in optimizing operating parameters to minimize roping in meltblown products.

Continuum insight into the effects of electrode design parameters on the electrochemical performance of lithium-ion batteries

Lithium-ion batteries energy and power density strongly depend on the type of active material and the electrode design parameters. An in-depth understanding of the effect of battery design parameters on their electrochemical performance is experimentally expensive and hence requires the utilization of cheaper continuum scale models. Here, using a lithium-ion cell composed of LiFePO4 cathode, Li4Ti5O12 anode and a porous separator filled with a liquid electrolyte as an example, we demonstrate the use of an experimentally validated pseudo-two-dimensional (P2D) model in one-dimension to explore the effects of different cell design parameters on the discharge capacity at different current rates. The model is simulated in two-dimensional to instantly visualize the concentration distribution of Li ions in the electrode at high discharge current rates. The continuum model unravels that the solution phase diffusion limitation is the main factor inhibiting the performance of thick electrodes at high current rates and the Li4Ti5O12 anode is the limiting electrode. These findings using continuum models provide guidance for and accelerate the optimization of electrode architecture for enhancing the performance of lithium-ion batteries.

Pulse-to-pulse coupling in cylindrical discharges

Abstract Several filamentary discharges can be applied to a combustible mixture, which can then ignite. The energy density of this discharge is a vital parameter, as it directly influences the local temperature rise and radical production. The goal of this article is to investigate how a previous discharge affects the energy density of a second discharge. To investigate the pulse-to-pulse coupling of filamentary discharges a one-dimensional numerical model is developed. In the developed model, the compressible Navier-Stokes equations are coupled to a plasma model. The plasma model is used to estimate the local energy density, while the compressible Navier-Stokes equations model the reactive flow. As a first step, skeletal air plasma chemistry is used, which includes fast gas heating, slow gas heating and the rapid generation of radicals. The skeletal plasma chemistry is combined with a detailed hydrogen combustion mechanism. Simulations in both air and hydrogen/air are conducted at several discharge energies and pressures. From the analysis of these results, we conclude that the main mechanism of pulse-to-pulse coupling is the reduction in molar density due to temperature rise.

Divergent Richtmyer–Meshkov instability under different shock strengths

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.

One-dimensional, multi-fluid model of the plasma-wall transition. II. Negative ions

The plasma-wall transition is investigated by a one-dimensional steady-state multifluid model, which was presented in detail in Part I [T. Gyergyek et al., AIP Adv. 14, 045201 (2024)]. In this work, the plasma-wall transition is analyzed for the case where the plasma consists of singly charged positive ions, electrons, and singly charged negative ions. When the temperature and initial density of the negative ions are varied, a transition between two types of solutions of the model is observed. We call them the low and high solution, with respect to the absolute value of the potential drop. When the density and temperature of the negative ions are above a critical value, the low solution is observed. As the mass of the positive ions increases, these critical values also increase, but only until the ion mass is below about 1000 electron masses. With larger ion masses, the critical density of the negative ions and the temperature no longer change. In the low solution, the potential drop in front of the sheath is determined by the negative ions and is smaller in absolute terms than in the case of the high solution, where the potential drop in front of the sheath is determined by the electrons. If the problem is analyzed on the pre-sheath scale, the transition between the low and high solution is very sharp. However, when the neutrality condition is replaced by the Poisson equation, this transition becomes blurred and the solutions of the model equations exhibit oscillations. The role of the smallness parameter is highlighted. It is shown how the initial electric field is determined. Deviation of the negative ion density profile from the Boltzmann relation is discussed.

Learning the dynamics of a one-dimensional plasma model with graph neural networks

Learning the dynamics of a one-dimensional plasma model with graph neural networks

Authentication with a one-dimensional CNN model using EEG-based brain-computer interface

Brain-computer interface (BCI) technology uses electroencephalogram (EEG) signals to create a direct interaction between the human body and its surroundings. Motor imagery (MI) classification using EEG signals is an important application that can help a rehabilitated or motor-impaired stroke patient perform certain tasks. Robust classification of these signals is an important step toward making the use of EEG more practical in many applications and less dependent on trained professionals. Deep learning methods have produced impressive results in BCI in recent years, especially with the availability of large electroencephalography (EEG) data sets. Dealing with EEG-MI signals is difficult because noise and other signal sources can interfere with the electrical amplitude of the brain, and its generalization ability is limited, so it is difficult to improve EEG classifiers. To address these issues, this paper presents a methodology based on one-dimensional convolutional neural networks (1-D CNN) for motor imagery (MI) recognition for the right hand, left hand, feet, and sedentary task. The proposed model is a lightweight model with fewer parameters and has an accuracy of 91.75%. Then, in an innovative exploitation of the four output classes, there is an idea that allows people with disabilities who are deprived of security measures, such as entering a secret code, to use the output classification, such as password codes. It is also an idea for a unique authentication system that is more secure and less vulnerable to theft or the like for a healthy person at the same time.

Simulation Study on Combustion Performance of Ammonia-Hydrogen Fuel Engines

Ammonia is a very promising alternative fuel for internal combustion engines, but there are some disadvantages, such as difficulty in ignition and slow combustion rate when ammonia is used alone. Aiming to address the problem of ammonia combustion difficulty, measures are proposed to improve ammonia combustion by blending hydrogen. A one-dimensional turbocharged ammonia-hydrogen engine simulation model was established, and the combustion model was corrected and verified. Using the verified one-dimensional model, the effects of different ratios of hydrogen to ammonia, different rotational speeds and loads on the combustion performance are investigated. The results show that the ignition delay and combustion duration is shortened with the increase of the hydrogen blending ratio. The appropriate amount of hydrogen blending can improve the brake’s thermal efficiency. With the increase in engine speed, increasing the proportion of hydrogen blending is necessary to ensure reliable ignition. In conclusion, the ammonia-hydrogen fuel engine has good combustion performance, but it is necessary to choose the appropriate hydrogen blending ratio according to the engine’s operating conditions and requirements.

Psychometric analysis of the GAD-7 questionnaire in Slovak helping professionals

The GAD-7 is a widely used screening tool for the measurement and diagnosis of symptoms of generalized anxiety disorder. It has been translated and validated across more than 20 cultural contexts. However, no study to date examined its psychometric properties in a Slovak sample, despite the fact that a Slovak translation exists. The purpose of the present study was to test psychometric properties and factor structure of GAD-7 in a general sample of Slovak helping professionals. It was hypothesized that a one-dimensional factor structure would be supported by the data, and that construct validity would be demonstrated. A total of 2239 participants (Mage = 42.20, SD = 14.30) from different helping professions (e.g., psychologists, teachers, special educators, medical doctors, nurses, speech-language pathologists) completed an online survey. A confirmatory factor analysis yielded satisfactory factor loadings and acceptable model fit of the tested one-dimensional model. This evidence was invariant by sex. Internal consistency coefficients indicated good reliability. Significant correlations were found between the GAD-7 and both negative and positive adjustment constructs, thus demonstrating convergent and discriminant validity, respectively. The results of this study add to the evidence on the GAD-7 and its applicability across cultures and support the use of a Slovak translation of the instrument.

A one-dimensional computational model for blood flow in an elastic blood vessel with a rigid catheter.

Strokes are one of the leading causes of death in the United States. Stroke treatment involves removal or dissolution of the obstruction (usually a clot) in the blocked artery by catheter insertion. A computer simulation to systematically plan such patient-specific treatments needs a network of about 105 blood vessels including collaterals. The existing computational fluid dynamic (CFD) solvers are not employed for stroke treatment planning as they are incapable of providing solutions for such big arterial trees in a reasonable amount of time. This work presents a novel one-dimensional mathematical formulation for blood flow modeling in an elastic blood vessel with a centrally placed rigid catheter. The governing equations are first-order hyperbolic partial differential equations, and the hypergeometric function needs to be computed to obtain the characteristic system of these hyperbolic equations. We employed the Discontinuous Galerkin method to solve the hyperbolic system and validated the implementation by comparing it against a well-established 3D CFD solver using idealized vessels and a realistic truncated arterial network. The results showed clinically insignificant differences in steady flow cases, with overall variations between 1D and 3D models remaining below 10%. Additionally, the solver accurately captured wave reflection phenomena at domain discontinuities in unsteady cases. A primary advantage of this model over 3D solvers is its ease in obtaining a discretized geometry of complex vasculatures with multiple arterial branches. Thus, the 1D computational model offers good accuracy and applicability in simulating complex vasculatures, demonstrating promising potential for investigating patient-specific endovascular interventions in strokes.

Influence of the disorder correlation length on localization and quantum state transference in tight-binding channels

We investigate in detail the transference of quantum states in a disordered channel. We consider a one-dimensional tight-binding model consisting of a source S connected to a receiver R throughout a disordered channel. The disorder distribution contains a single tunable spatial correlation length. We demonstrate that the disorder correlation length plays a relevant role within the localization properties of the channel. The hopping parameter between the sites S and R and the channel are also adjustable parameters. We investigate the possibility of transference of quantum states along this quantum channel model and describe the optimal conditions for the occurrence of a high fidelity process.

A one-dimensional model of air-cooled proton exchange membrane fuel cell stack integrating fan arrangement and operational characteristics

Air-cooled proton exchange membrane fuel cell stack’s performance can be greatly affected by the arrangement and operational characteristics of the fans that generate the air flow. However, the influence mechanisms are complex and poorly understood. In this study, a one-dimensional analytical model specifically for air-cooled stacks integrating important fan features is developed to quickly (e.g. within 5 min for a 100-cell stack) and accurately predict the water and thermal states inside stacks and stack performance under various fan arrangements and operational characteristics. The model accuracy was validated against the experimental results of a 95-cell air-cooled stack, including the stack polarization curves, temperature distribution and air flow rates at different fan’s duty cycles. The model results showed that for high air flow resistance stacks, the air flow rate and maximum net power for fans arrangement in series are higher than those in parallel by about 10% and 0.5%, respectively. Moreover, integrating a single large fan can be better than two small fans as the former induces a higher air flow rate and static pressure. On the other hand, altering the air flow channel length or depth changes the air flow resistance in stacks, leading to a shift of the working point for a fixed fan at a certain duty cycle and greatly influencing stack performance. This one-dimensional air-cooled stack model can be a powerful tool to facilitate stack design and optimization.

Friction models of one-dimensional earthquakes

Abstract A number of fundamental characteristics of earthquake physics are reproduced by simple stick-slip friction models. These include creep motion, stick/slip periodic earthquakes, reduced frequency of occurrence for more energetic quakes, ground velocity proportional to slip duration, and ground displacement proportional to fault length. By confining attention to one dimension, these results are obtained analytically. Though many earthquake characteristics cannot be reproduced in a one-dimensional model, our simple approach nevertheless has pedagogical value in providing insight into some of the complicated dynamics of earthquakes.

Pressure evaluation in highly porous medium hydrodynamic bearings

This paper presents an experimental investigation into lift generation during the tangential motion of an inclined surface over a compressible porous layer, focusing on an exceptionally slow sliding speed, a condition that has not been considered in previous studies. Specifically, we validated Pascovici's one-dimensional lubrication model for an inclined slider under the above condition. Additionally, we explore the use of woven fibrous material for soft porous lubrication, broadening the range of media for future studies.

Non-invasive monitoring of microalgae cultivations using hyperspectral imager

AbstractHigh expectations are placed on microalgae as a sustainable source of valuable biomolecules. Robust methods to control microalgae cultivation processes are needed to enhance their efficiency and, thereafter, increase the profitability of microalgae-based products. To meet this need, a non-invasive monitoring method based on a hyperspectral imager was developed for laboratory scale and afterwards tested on industrial scale cultivations. In the laboratory experiments, reference data for microalgal biomass concentration was gathered to construct 1) a vegetation index-based linear regression model and 2) a one-dimensional convolutional neural network model to resolve microalgae biomass concentration from the spectral images. The two modelling approaches were compared. The mean absolute percentage error (MAPE) for the index-based model was 15–24%, with the standard deviation (SD) of 13-18 for the different species. MAPE for the convolutional neural network was 11–26% (SD = 10–22). Both models predicted the biomass well. The convolutional neural network could also classify the monocultures of green algae by species (accuracy of 97–99%). The index-based model was fast to construct and easy to interpret. The index-based monitoring was also tested in an industrial setup demonstrating a promising ability to retrieve microalgae-biomass-based signals in different cultivation systems.