Acid-rock reaction kinetics in a two-scale model based on reaction order correction

The reaction order plays a crucial role in evaluating the response rate of acid-rock.However,the conventional two-scale model typically assumes that the reaction order is constant as one,which can lead to significant deviations from reality.To address this issue,this study proposes a novel multi-order dynamic model for acid-rock reaction by combining rotating disk experimental data with theoretical derivation.Through numerical simulations,this model allows for the investigation of the impact of acidification conditions on different orders of reaction,thereby providing valuable insights for on-site construction.The analysis reveals that higher response orders require higher optimal acid liquid flow rates,and lower optimal H+diffusion coefficients,and demonstrate no significant correlation with acid concentration.Consequently,it is recommended to increase the displacement and use high-viscosity acid for reservoirs with high calcite content,while reducing the displacement and using low-viscosity acid for reservoirs with high dolomite content.

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Meta-Auto-Decoder:a Meta-Learning-Based Reduced Order Model for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.

Effect of distribution shape on the melting transition, local ordering,and dynamics in a model size-polydisperse two-dimensional fluid

We study the effect of particle size polydispersity(δ) on the melting transition(T*), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian(G) and uniform(U) distribution functions.For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity,the value of T*initially increases due to improved packing efficiency(φ) followed by a decrease and terminates at δ ≈8%(U-system) and 14%(G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which φ drops suddenly coincides with the peak of the heat capacity(CP) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter(Q_6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T –δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems;however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Estimation of Landfill Gas and Its Renewable Energy Potential from the Polesgo Controlled Landfill Using First-Order Decay (FOD) Models

Methane generation in landfills and its inadequate management represent the major avoidable source of anthropogenic methane today. This paper models methane production and the potential resources expected (electrical energy production and potential carbon credits from avoided CH4 emissions) from its proper management in a municipal solid waste landfill located in Ouagadougou, Burkina Faso. The modeling was carried out using two first-order decay (FOD) models (LandGEM V3.02 and SWANA) using parameters evaluated on the basis of the characteristics of the waste admitted to the landfill and weather data for the site. At the same time, production data have been collected since 2016 in order to compare them with the model results. The results obtained from these models were compared to experimental one. For the simulation of methane production, the SWANA model showed better consistency with experimental data, with a coefficient of determination (R²) of 0.59 compared with the LandGEM model, which obtained a coefficient of 0.006. Thus, despite the low correlation values linked to the poor consistency of experimental data, the SWANA model models methane production much better than the LandGEM model. Thus, despite the low correlation values linked to the poor consistency of the experimental data, the SWANA model models methane production much better than the LandGEM V3.02 model. It was noted that the poor consistency of the experimental data justifies these low coefficients, and that they can be improved in the future thanks to ongoing in situ measurements. According to the SWANA model prediction, in 27 years of operation a biogas plant with 33% electrical efficiency using biogas from the Polesgo landfill would avoid 1,340 GgCO2e. Also, the evaluation of revenues due to electricity and carbon credit gave a total revenue derived from methane production of US$27.38 million at a cost of US$10.5/tonne CO2e.

Pedestrian lane formation with following–overtaking model and measurement of system order

Pedestrian self-organizing movement plays a significant role in evacuation studies and architectural design.Lane formation,a typical self-organizing phenomenon,helps pedestrian system to become more orderly,the majority of following behavior model and overtaking behavior model are imprecise and unrealistic compared with pedestrian movement in the real world.In this study,a pedestrian dynamic model considering detailed modelling of the following behavior and overtaking behavior is constructed,and a method of measuring the lane formation and pedestrian system order based on information entropy is proposed.Simulation and analysis demonstrate that the following and avoidance behaviors are important factors of lane formation.A high tendency of following results in good lane formation.Both non-selective following behavior and aggressive overtaking behavior cause the system order to decrease.The most orderly following strategy for a pedestrian is to overtake the former pedestrian whose speed is lower than approximately 70%of his own.The influence of the obstacle layout on pedestrian lane and egress efficiency is also studied with this model.The presence of a small obstacle does not obstruct the walking of pedestrians;in contrast,it may help to improve the egress efficiency by guiding the pedestrian flow and mitigating the reduction of pedestrian system orderliness.

A novel order-reduced thermal-coupling electrochemical model for lithium-ion batteries

Although the single-particle model enhanced with electrolyte dynamics(SPMe)is simplified from the pseudo-twodimensional(P2D)electrochemical model for lithium-ion batteries,it is difficult to solve the partial differential equations of solid–liquid phases in real-time applications.Moreover,working temperatures have a heavy impact on the battery behavior.Hence,a thermal-coupling SPMe is constructed.Herein,a lumped thermal model is established to estimate battery temperatures.The order of the SPMe model is reduced by using both transfer functions and truncation techniques and merged with Arrhenius equations for thermal effects.The polarization voltage drop is then modified through the use of test data because its original model is unreliable theoretically.Finally,the coupling-model parameters are extracted using genetic algorithms.Experimental results demonstrate that the proposed model produces average errors of about 42 mV under 15 constant current conditions and 15 mV under nine dynamic conditions,respectively.This new electrochemicalthermal coupling model is reliable and expected to be used for onboard applications.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

Aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders:progress of experimental models based on disease pathogenesis

Neuromyelitis optica spectrum disorders are neuroinflammatory demyelinating disorders that lead to permanent visual loss and motor dysfunction.To date,no effective treatment exists as the exact causative mechanism remains unknown.Therefore,experimental models of neuromyelitis optica spectrum disorders are essential for exploring its pathogenesis and in screening for therapeutic targets.Since most patients with neuromyelitis optica spectrum disorders are seropositive for IgG autoantibodies against aquaporin-4,which is highly expressed on the membrane of astrocyte endfeet,most current experimental models are based on aquaporin-4-IgG that initially targets astrocytes.These experimental models have successfully simulated many pathological features of neuromyelitis optica spectrum disorders,such as aquaporin-4 loss,astrocytopathy,granulocyte and macrophage infiltration,complement activation,demyelination,and neuronal loss;however,they do not fully capture the pathological process of human neuromyelitis optica spectrum disorders.In this review,we summarize the currently known pathogenic mechanisms and the development of associated experimental models in vitro,ex vivo,and in vivo for neuromyelitis optica spectrum disorders,suggest potential pathogenic mechanisms for further investigation,and provide guidance on experimental model choices.In addition,this review summarizes the latest information on pathologies and therapies for neuromyelitis optica spectrum disorders based on experimental models of aquaporin-4-IgG-seropositive neuromyelitis optica spectrum disorders,offering further therapeutic targets and a theoretical basis for clinical trials.

A NOVEL STOCHASTIC HEPATITIS B VIRUS EPIDEMIC MODEL WITH SECOND-ORDER MULTIPLICATIVE α-STABLE NOISE AND REAL DATA

This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.

Numerical Simulation and Parameter Estimation of Fractional-Order Dynamic Epidemic Model for COVID-19

The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.

Dynamic Modeling and Experimental Verification of an RPR Type Compliant Paralle Mechanism with Low Orders

Efficiency of calculating a dynamic response is an important point of the compliant mechanism for posture adjustment.Dynamic modeling with low orders of a 2R1T compliant parallel mechanism is studied in the paper.The mechanism with two out-of-plane rotational and one lifting degrees of freedom(DoFs)plays an important role in posture adjustment.Based on elastic beam theory,the stiffness matrix and mass matrix of the beam element are established where the moment of inertia is considered.To improve solving efficiency,a dynamic model with low orders of the mechanism is established based on a modified modal synthesis method.Firstly,each branch of the RPR type mechanism is divided into a substructure.Subsequently,a set of hypothetical modes of each substructure is obtained based on the C-B method.Finally,dynamic equation of the whole mechanism is established by the substructure assembly.A dynamic experiment is conducted to verify the dynamic characteristics of the compliant mechanism.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

Establishment of a Fractional Order COVID-19 Model and Its Feasibility Analysis

This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.

A Note on an Order Level Inventory Model with Varying Two-Phased Demand and Time-Proportional Deterioration

The main purpose of this paper is to generalize the effect of two-phased demand and variable deterioration within the EOQ (Economic Order Quantity) framework. The rate of deterioration is a linear function of time. The two-phased demand function states the constant function for a certain period and the quadratic function of time for the rest part of the cycle time. No shortages as well as partial backlogging are allowed to occur. The mathematical expressions are derived for determining the optimal cycle time, order quantity and total cost function. An easy-to-use working procedure is provided to calculate the above quantities. A couple of numerical examples are cited to explain the theoretical results and sensitivity analysis of some selected examples is carried out.

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Large multimodal models assist in psychiatry disorders prevention and diagnosis of students

Students are considered one of the groups most affected by psychological pro-blems.Given the highly dangerous nature of mental illnesses and the increasing-ly serious state of global mental health,it is imperative for us to explore new me-thods and approaches concerning the prevention and treatment of mental illne-sses.Large multimodal models(LMMs),as the most advanced artificial intelligen-ce models(i.e.ChatGPT-4),have brought new hope to the accurate prevention,diagnosis,and treatment of psychiatric disorders.The assistance of these models in the promotion of mental health is critical,as the latter necessitates a strong foundation of medical knowledge and professional skills,emotional support,stigma mitigation,the encouragement of more honest patient self-disclosure,reduced health care costs,improved medical efficiency,and greater mental health service coverage.However,these models must address challenges related to health,safety,hallucinations,and ethics simultaneously.In the future,we should address these challenges by developing relevant usage manuals,accountability rules,and legal regulations;implementing a human-centered approach;and intelligently upgrading LMMs through the deep optimization of such models,their algorithms,and other means.This effort will thus substantially contribute not only to the maintenance of students’health but also to the achievement of global sustainable development goals.

A Second-Order Image Denoising Model for Contrast Preservation

In this work,we propose a second-order model for image denoising by employing a novel potential function recently developed in Zhu(J Sci Comput 88:46,2021)for the design of a regularization term.Due to this new second-order derivative based regularizer,the model is able to alleviate the staircase effect and preserve image contrast.The augmented Lagrangian method(ALM)is utilized to minimize the associated functional and convergence analysis is established for the proposed algorithm.Numerical experiments are presented to demonstrate the features of the proposed model.

Exploiting fly models to investigate rare human neurological disorders

Rare neurological diseases,while individually are rare,collectively impact millions globally,leading to diverse and often severe neurological symptoms.Often attributed to genetic mutations that disrupt protein function or structure,understanding their genetic basis is crucial for accurate diagnosis and targeted therapies.To investigate the underlying pathogenesis of these conditions,researchers often use non-mammalian model organisms,such as Drosophila(fruit flies),which is valued for their genetic manipulability,cost-efficiency,and preservation of genes and biological functions across evolutionary time.Genetic tools available in Drosophila,including CRISPR-Cas9,offer a means to manipulate gene expression,allowing for a deep exploration of the genetic underpinnings of rare neurological diseases.Drosophila boasts a versatile genetic toolkit,rapid generation turnover,and ease of large-scale experimentation,making it an invaluable resource for identifying potential drug candidates.Researchers can expose flies carrying disease-associated mutations to various compounds,rapidly pinpointing promising therapeutic agents for further investigation in mammalian models and,ultimately,clinical trials.In this comprehensive review,we explore rare neurological diseases where fly research has significantly contributed to our understanding of their genetic basis,pathophysiology,and potential therapeutic implications.We discuss rare diseases associated with both neuron-expressed and glial-expressed genes.Specific cases include mutations in CDK19 resulting in epilepsy and developmental delay,mutations in TIAM1 leading to a neurodevelopmental disorder with seizures and language delay,and mutations in IRF2BPL causing seizures,a neurodevelopmental disorder with regression,loss of speech,and abnormal movements.And we explore mutations in EMC1 related to cerebellar atrophy,visual impairment,psychomotor retardation,and gain-of-function mutations in ACOX1 causing Mitchell syndrome.Loss-of-function mutations in ACOX1 result in ACOX1 deficiency,characterized by very-long-chain fatty acid accumulation and glial degeneration.Notably,this review highlights how modeling these diseases in Drosophila has provided valuable insights into their pathophysiology,offering a platform for the rapid identification of potential therapeutic interventions.Rare neurological diseases involve a wide range of expression systems,and sometimes common phenotypes can be found among different genes that cause abnormalities in neurons or glia.Furthermore,mutations within the same gene may result in varying functional outcomes,such as complete loss of function,partial loss of function,or gain-of-function mutations.The phenotypes observed in patients can differ significantly,underscoring the complexity of these conditions.In conclusion,Drosophila represents an indispensable and cost-effective tool for investigating rare neurological diseases.By facilitating the modeling of these conditions,Drosophila contributes to a deeper understanding of their genetic basis,pathophysiology,and potential therapies.This approach accelerates the discovery of promising drug candidates,ultimately benefiting patients affected by these complex and understudied diseases.

Effects of Polygala fallax Hemsl Water Extract on a Mouse Model of Gastric Motility Disorders

[Objectives]To explore the effects of Polygona fallax Hemsl water extract on gastrointestinal motility in normal mice and gastric motility disorder model mice and approximate mechanism.[Methods]Using normal mice and mice with gastric motility disorders(modeled with atropine),the effects of different mass concentration groups of P.fallax Hemsl water extract(0.125,0.250,0.500 g/mL)and domperidone groups on gastric residual rate,small intestine propulsion rate,serum motilin(MLT),vasoactive intestinal peptide(VIP),and tissue morphology were studied.[Results]There was a highly significant difference(P<0.01)in the small intestine propulsion rate of liquid in normal mice among the different concentration groups of P.fallax Hemsl water extract compared to the blank group.The small intestine propulsion rate and gastric residue rate of semi-solid paste were statistically significant compared to the blank group(P<0.05).Among them,there was a highly significant difference between the high concentration group(67.75%±7.65%,46.5%±10.62%)and the medium concentration group(60.90%±5.87%,59.27%±7.82%)(P<0.01).There was statistical significance in normal mouse serum MLT content in the high concentration group(P<0.05).There was no effect on serum VIP levels in normal mice;no effect on the morphology of stomach and intestinal tissues of normal mice.The small intestine propulsion rate and gastric residue rate of liquid and semi-solid paste in mice with gastric motility disorders were statistically significant compared to the atropine group,with extremely significant differences(P<0.01).[Conclusions]P.fallax Hemsl water extract has a promoting effect on gastrointestinal motility.One of the specific mechanisms by which P.fallax Hemsl promotes gastrointestinal motility in normal mice may be related to the content of MLT in mouse serum.The mechanism of action in atropine induced gastric paresis mice may be related to the reactivation of M receptors,and the action mechanism of P.fallax Hemsl does not change the original histological basis.It can be inferred that P.fallax Hemsl water extract has a synergistic effect on promoting gastrointestinal motility through other mechanisms,but it is not fully understood and further in-depth research is needed.