Exponential Approach Research Articles

High-order energy stable variable-step schemes for the time-fractional Cahn–Hilliard model

Based on the Alikhanov formula of the Caputo derivative and the exponential scalar auxiliary variable approach, two different second-order stable numerical schemes are constructed for the time-fractional Cahn–Hilliard model, including the nonlinear L2-1σ scheme and the linear L2-1σ-ESAV scheme. Applying the discrete gradient structure, we construct the asymptotically compatible energies and the associated energy dissipation laws of these two schemes for the time-fractional Cahn–Hilliard model. Several experiments are carried out to demonstrate the accuracy of our schemes and compare their computational efficiency, as well as to investigate the coarsening dynamics of the time-fractional Cahn–Hilliard model with different adaptive time-stepping strategies. In the long-time simulations, the linear L2-1σ-ESAV scheme may be more costly than the nonlinear L2-1σ scheme although the linear scheme may take less time at each time level. It is observed that the energy of the L2-1σ-ESAV scheme prones to produce small fluctuations when large time steps are used.

Exploring localized waves and different dynamics of solitons in (2 + 1)-dimensional Hirota bilinear equation: a multivariate generalized exponential rational integral function approach

Exploring localized waves and different dynamics of solitons in (2 + 1)-dimensional Hirota bilinear equation: a multivariate generalized exponential rational integral function approach

Soliton unveilings in optical fiber transmission: Examining soliton structures through the Sasa–Satsuma equation

The exploration of higher-order and multicomponent extensions of the nonlinear Schrödinger equation holds significant importance across diverse applications, notably within the field of optics. Among these equations, the integrable Sasa–Satsuma equation stands out for its captivating soliton solutions. The Sasa–Satsuma equation serves as a mathematical representation for describing the propagation of femtosecond light pulses through optical fibers. The breather, multiwave, combined dark–bright, singular, dark, bright and periodic singular optical soliton solutions are derived in this paper by using the 1φ(ϑ),φ′(ϑ)φ(ϑ) and multivariate generalized exponential rational integral function approach. Furthermore, the paper emphasizes the essential fiber parameters essential for the emergence of these structures and offers visual representations of chosen solutions to elucidate their physical characteristics. The novelty of this work lies in the inaugural application of these methods to the Sasa–Satsuma equation and gives a significant advancement in the understanding of optical phenomena. This study not only opens avenues for further research but also introduces a fresh perspective on the Sasa–Satsuma model in the field of nonlinear physics with its applications in optical systems.

Analysis and Forecasting of Consumer Price Index (CPI) in Kenya and South Africa using Holt Winter Model

In this paper, Holt-Winters exponential smoothing approach is applied to model and forecast monthly CPI in Kenya and South Africa. Monthly data from January 2000 to December 2023 was obtained from Central Bank of Kenya and South Africa department of statistics. Time series decomposition showed that the trend component is the most dominant component in both countries. Kenya Holt-Winters estimated model has parameters 0.6756, 0.0077 and 1 for level smoothing, trend smoothing and seasonal smoothing respectively. On the other hand, South Africa estimated model has parameters 0.8917, 0.1057 and 1 for level smoothing, trend smoothing and seasonal smoothing respectively. The estimated models are efficient and effective as on average the fitted values are less than one percent off the observed values. The initial values for level smoothing, trend smoothing and seasonal smoothing are approximately equal in both countries. The estimated models are then used to predict CPI next twelve months. Over the forecast period, South Africa will experience a lower index as compared to Kenya. In both countries, it’s expected that monthly CPI will rise.

A 2TLNS-based exponential TODIM-EDAS approach for evaluating sustainable development of cross-border e-commerce platforms under uncertainty

In the context of globalization, cross-border e-commerce platforms have become the main way for enterprises to achieve international trade transformation and overseas investment. From this, it can be seen that cross-border e-commerce platforms are of great importance to the development of enterprises, and the development of cross-border e-commerce platforms is also a necessary choice for the development of the times. In the new era, in order to make cross-border e-commerce platforms better serve enterprises and bring economic benefits to their development. The sustainable development capability evaluation of third-party cross-border e-commerce (TPCBEC) platform is a MAGDM. Recently, the Exponential TODIM (ExpTODIM) technique and Evaluation Based on Distance from Average Solution (EDAS) technique has been employed to cope with MAGDM issues. The 2-tuple linguistic neutrosophic sets (2TLNSs) are employed as a tool for portraying uncertain information during the sustainable development capability evaluation of TPCBEC platform. In this paper, the 2-tuple linguistic neutrosophic number Exponential TODIM-EDAS (2TLNN-ExpTODIM-EDAS) technique is implemented to manage the MAGDM under 2TLNSs. Finally, a numerical study for sustainable development capability evaluation of TPCBEC platform is constructed to validate the implemented technique. Thus, the main advantages of the proposed 2TLNN-ExpTODIM-EDAS technique are outlined: (1) the proposed 2TLNN-ExpTODIM-EDAS technique not only handles the distances information from the 2TLNNAS, but also portrays the DMs’ psychological behavior during the sustainable development capability evaluation of TPCBEC platform. (2) the proposed 2TLNN-ExpTODIM-EDAS technique analyze the behavior of the TODIM technique and EDAS technique as MADM techniques when they are hybridized.

Adaptive Fuzzy Sliding Mode Control and Dynamic Modeling of Flap Wheel Polishing Force Control System

Polishing force is one of the key process parameters in the polishing process of blisk blades, and its control accuracy will affect the surface quality and processing accuracy of the workpiece. The contact mechanism between the polishing surface and flap wheel was analyzed, and the calculation model of the polishing force and nonlinear dynamic model of the polishing force control system was established. Considering the influence of friction characteristics, parameter perturbation, and nonlinear dead zone on the control accuracy of the polishing force system, an adaptive fuzzy sliding mode controller (AFSMC) was designed. AFSMC uses a fuzzy system to adaptively approximate the nonlinear function terms in the sliding mode control law, adopts an exponential approach law in the switching control part of the sliding mode control (SMC), and designs the adaptive law for adjustable parameters in the fuzzy system based on the Lyapunov Theorem. Simulation and experimental results show that the designed AFSMC has a fast dynamic response, strong anti-interference ability, and high control accuracy, and it can reduce SMC high-frequency chatter. Polishing experiments show that compared with traditional PID, AFSMC can improve the form and position accuracy of the blade by 42% and reduce the surface roughness by 50%.

An SMC-Based Accurate and Robust Load Speed Control Method for Elastic Servo System

In this paper, a modified sliding mode speed controller is designed in order to improve the load speed control performance of an elastic motor drive system with internal and external disturbances. Firstly, based on the load speed deviation and its first-order and second-order differentials, a two-dimensional sliding surface function is presented. The parameters of the sliding surface are determined by a novel particle swarm optimization (PSO) method. The method has improved inertia weights and evaluation functions, which can improve the accuracy and efficiency of the parameter search and enhance the immunity and robustness of the system. Secondly, on the basis of the integral of time-weighted absolute error (ITAE) criterion, the parameters of the exponential approach law are determined, which improves the tracking accuracy. Finally, the designed sliding mode control (SMC) with high tracking accuracy, fast dynamics, and strong robustness is verified by both simulations and experiments.

Exponential Combination of a and e/g Intracellular Peptide Libraries Identifies a Selective ATF3 Inhibitor.

Activating transcription factor 3 (ATF3) is an activation transcription factor/cyclic adenosine monophosphate (cAMP) responsive element-binding (CREB) protein family member. It is recognized as an important regulator of cancer progression by repressing expression of key inflammatory factors such as interferon-γ and chemokine (C-C motif) ligand 4 (CCL4). Here, we describe a novel library screening approach that probes individual leucine zipper components before combining them to search exponentially larger sequence spaces not normally accessible to intracellular screening. To do so, we employ two individual semirational library design approaches and screen using a protein-fragment complementation assay (PCA). First, a 248,832-member library explored 12 amino acid positions at all five a positions to identify those that provided improved binding, with all e/g positions fixed as Q, placing selection pressure onto the library options provided. Next, a 59,049-member library probed all ten e/g positions with 3 options. Similarly, during e/g library screening, a positions were locked into a generically bindable sequence pattern (AIAIA), weakly favoring leucine zipper formation, while placing selection pressure onto e/g options provided. The combined a/e/g library represents ∼14.7 billion members, with the resulting peptide, ATF3W_aeg, binding ATF3 with high affinity (Tm = 60 °C; Kd = 151 nM) while strongly disfavoring homodimerization. Moreover, ATF3W_aeg is notably improved over component PCA hits, with target specificity found to be driven predominantly by electrostatic interactions. The combined a/e/g exponential library screening approach provides a robust, accelerated platform for exploring larger peptide libraries, toward derivation of potent yet selective antagonists that avoid homoassociation to provide new insight into rational peptide design.

Dynamic simulation of traveling wave solutions for the differential-difference Burgers’ equation utilizing a generalized exponential rational function approach

Dynamic simulation of traveling wave solutions for the differential-difference Burgers’ equation utilizing a generalized exponential rational function approach

A second-order exponential integration constraint energy minimizing generalized multiscale method for parabolic problems

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial discretization of the model problem using constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). This approach consists of two stages. First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. The multiscale basis functions are obtained in the second stage using the auxiliary space by solving local energy minimization problems over the oversampling domains. The basis functions have exponential decay outside the corresponding local oversampling regions. We shall consider the first and second-order explicit exponential Runge-Kutta approach for temporal discretization and to build a fully discrete numerical solution. The exponential integration strategy for the time variable allows us to take full advantage of the CEM-GMsFEM as it enables larger time steps due to its stability properties. We derive the error estimates in the energy norm under the regularity assumption. Finally, we will provide some numerical experiments to sustain the efficiency of the proposed method.

Dynamic study of new soliton solutions of time-fractional longitudinal wave equation using an analytical approach

In this study, the modified exponential approach is used to investigate the fractional order longitudinal wave equation in a magneto-elastic circular rod, which represents the nonlinear interplay between dispersion and longitudinal wave velocity depending on the rod’s material and geometry. The time-fractional order is used in the standpoint of conformable derivative. Comprehensive and descriptive waveform solutions, including kink-shaped, bell-shaped, and bright bell-shaped solitons, are obtained. The produced soliton solutions are advanced, unique, developed, and crucial. To demonstrate the physical appearance of the obtained solutions, 2D, 3D, and contour graphs of some of the obtained solutions are plotted. The extracted solutions demonstrate the physical significance of the model and express the pressure and electrostatic potential for the longitudinal wave equation and can be used to elucidate more complicated nonlinear models of classical and fractional order. The obtained results are helpful in finding the amplitude of tsunami waves which is of great interest to researchers in the field of ocean engineering. If a tsunami extends across a large area, it becomes a manifestation of solitons. The comparison of the obtained solutions is also given in the form of remarks 1 and 2 which shows the novelty of our work.

Fixed-time tracking control of manipulators based on non-singular fast terminal sliding surface

As for the problem of trajectory tracking of a multi-joint serial manipulator, a novel fixed-time control scheme is proposed based on non-singular fast terminal sliding mode control. By employing a fast terminal sliding mode surface, we solve the singularity problem existed in traditional terminal sliding mode surface. In the meantime, in order to improve the rapidity of the system, the fixed-time control is incorporated with the fast terminal sliding mode surface control. Theoretical analysis proves that the proposed control scheme guarantees that better tracking performance is obtained, and its convergence time upper limit is not affected by the initial states. In addition, a reaching law with the exponential approach characteristic is added to the control law, which effectively reduces the chattering phenomenon in the controller design. Finally, the effectiveness and feasibility of the designed controller are verified through a numerical simulation.

Calibrating a Heat Transfer Model for Baled Switchgrass Using Heat Generation

HighlightsHeat and mass transfer in baled switchgrass was modeled based on thermal conductivity and internal heat generation.Model calibration was performed through a 60-day storage evaluation of baled switchgrass in an environmental chamber.Empirical models of heat generation and DML were developed based on thermal conductivity and aerobic respiration.Model validation was performed based on an energy balance and the aerobic respiration rate of switchgrass.Abstract. This study characterizes heat transfer within baled switchgrass through the development of a two-dimensional heat conduction model and an exponential drying approach to predict moisture content. The model was simulated using the finite difference method while accounting for the effect of internal heat generation to improve prediction accuracy. Model calibration was performed using rectangular bales of switchgrass (102 x 46 x 36 cm) stored in a controlled environmental chamber for 60 days at a fixed temperature and relative humidity. The heat and mass transfer model was implemented as an inverse model to empirically estimate heat generation and dry matter loss (DML). Internal heat generation and dry matter losses were also assessed using previously published models describing the aerobic respiration rate of switchgrass. Both heat generation models were in close agreement at a nominal moisture content of 10% w.b. (R2 = 0.9542) but deviated at nominal moisture contents of 20% to 40% w.b. (R2 < 0.7543). DML simulated using the numerical model closely agreed with the DML measured in the storage evaluation (R2 > 0.9060), indicating sufficient DML estimates through the conduction model and exponential drying approach. DML simulated through the published aerobic respiration model deviated to a greater extent, particularly at the highest moisture treatment (R2 = 0.4340), indicating an insufficient consideration of the various biochemical processes occurring at elevated levels of moisture and density. The results of this study provide a framework for the development of post-harvest quality models to optimize the storage, drying, and bioconversion of baled biomass feedstocks. Keywords: Bales, Heat and mass transfer, Heat transfer model, Storage losses, Switchgrass.

Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach

<p>The keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). In this paper, we employ the exponential scalar auxiliary variable (E-SAV) method to solve a semi-linear wave equation. By defining two different variables and combining the Crank−Nicolson scheme, two semi-discrete schemes are proposed, both of which are second-order and maintain Hamiltonian conservation. Two numerical experiments are presented to verify the reliability of the theory.</p>

κ-Exponential Inflation

We investigate a possible inflationary scenario where the expansion of the universe is driven by a slow evolution of a homogeneous single scalar field, whose potential V (φ) is given by an unusual κ-generalized power law. Within the slow-roll approximation we obtain several of the main predictions of the model, as the scalar spectral index, the tensor-to-scalar ratio, the number of e-folds, and the local non-Gaussianity. We also show that this model admits a much wider set of solutions than the usual exponential approach, and that their theoretical predictions are contemplated by the observational data.

Interval-Valued p,q-Rung Orthopair Fuzzy Exponential TODIM Approach and Its Application to Green Supplier Selection

An interval-valued q-rung orthopair fuzzy set (IVqrOFS) is a robust and esteemed model in managing imprecise information, utilizing a controllable parameter q≥1. Expanding its applicability, we propose a refinement to it, termed the interval-valued p,q-rung orthopair fuzzy set, denoted IVp,qrOFS. This advancement enables the handling of scenarios where varied assessment levels for membership and non-membership grades are necessary, a challenge unaddressed by existing extensions of interval-valued intuitionistic fuzzy sets. We establish the fundamental mathematical operations for the IVp,qrOFS and explore their key properties. To compare interval-valued p,q-rung orthopair fuzzy (IVp,qrOF) numbers, a novel score function is put forward and compared to the known IVqrOFS-based score functions to determine its viability. Moreover, we present IVp,qrOF aggregation operators (AOs), accompanied by rigorous proof of their essential characteristics, including boundedness, monotonicity, and symmetry. This study introduces the interaction of IVp,qrOF criteria through the inter-criteria correlation (CRITIC) approach. This method determines criteria weights based on the proposed distance measurements and the score function. The CRITIC method is integrated with the exponential TODIM approach (exp-TODIM), resulting in an innovative decision-making framework that is less susceptible to parameter fluctuations and showcases a high stability. An illustrative example of selecting a suitable supplier is provided to demonstrate the practical application of the developed exp-TODIM approach. Finally, a sensitivity analysis is conducted to exhibit the method’s stability, and a comparative analysis is performed to elucidate its strengths and advantages.

The information content of sentiment indices in forecasting Value at Risk and Expected Shortfall: a Complete Realized Exponential GARCH-X approach

The aim of this paper is to investigate the impact of public sentiment on tail risk forecasting. In this framework, we extend the Realized Exponential GARCH model to directly incorporate information from realized volatility measures and exogenous variables, thus resulting in a novel dynamically complete specification denoted as the Complete REGARCH-X model. Several sentiment indices related to social media and journal articles regarding the economy and stock market volatility are considered as potential drivers of volatility dynamics. An application to the prediction of daily Value-at-Risk and Expected Shortfall for the Standard & Poor’s 500 index provides evidence that combining the information content of realized volatility and sentiment measures can lead to significant accuracy gains in forecasting tail risk.

Landscape Analysis of Traditional Tribal Healers and Their Healing Practices in the Tribal-dominated States of India

Tribal communities have a rich history as some of the earliest inhabitants of the Indian subcontinent, living in harmony with nature for thousands of years. These indigenous or ethnic groups are spread throughout India, with significant concentrations in states like Chhattisgarh (30.5%), Jharkhand (26.0%), Odisha (22.8%), Madhya Pradesh (21.0%), Gujarat (14.7%), Rajasthan (13.4%), and Maharashtra (9.3%). In the peninsular region, notable tribal groups include Bhils, Santhals, Gonds, Ho, Kondh, Kols, Mundas, and Kharia, while in the northeast region, the prominent ones are Nagas, Mizos, Mikris, and Kukis. However, their access to healthcare is hindered by limited infrastructure, illiteracy, poverty, unemployment, socio-economic challenges, and marginalization. As a result, tribal communities often turn to traditional healers and indigenous medicinal practices, giving preference to traditional healing over modern healthcare options. Tribal traditional healers lack formal medical degrees, but their deep connection with indigenous communities makes them a preferred choice for healthcare. They are easily accessible to tribal populations and offer cost-effective services. These healers rely on their extensive traditional knowledge and skills, utilizing locally available medicinal plants, animal, and mineral substances, and incorporating specific ritual practices in their treatment methods for patients. Tribal healers are integral components of the available local healthcare system and play a critical role in delivering primary care services. The primary objective of this landscape analysis was to conduct a comprehensive examination of the socio-economic status, healing practices, and knowledge transfer methods of tribal healers and folk practitioners. Additionally, it aimed to create an evidence-based roadmap for their integration into the mainstream through upskilling, certificating, and federating the tribal healers. The study was ethnographic descriptive cross-sectional research conducted between May 15th and September 30th, 2023. The study comprised 1649 participants, encompassing Herbalists, Spiritual Healers, Diviners, Bone Setters, and Traditional Birth Attendants hailing from 43 districts in 7 tribal dominated states predominantly inhabited by tribal communities, namely Chhattisgarh, Jharkhand, Odisha, Madhya Pradesh, Maharashtra, Assam, and Arunachal Pradesh. Data collection occurred across 43 districts situated within the aforementioned states. The selection of tribal healers was done using an Exponential non-discriminative snowball non-probability sampling approach. The research methodology encompassed ethnographic research, interviews with healers, and documentary analysis. The analysis showcased the diversity of traditional healers, representing about 240 tribes, and emphasized the rich cultural and regional variations in their healing practices. The study involved tribal healers with an average age of 52.6 years, of which 82.4% were above 40 years old. These healers had varied roles and expertise, such as general herbalists, bone setters, Ojhas, or Dondai, each employing distinct diagnostic methods and treatments for the indigenous population. About 53.9% of folk healers were skilled in indigenous medicine, using natural substances for healthcare. Additionally, 42.5% of religious practitioners integrated social, cultural, and religious beliefs into their treatments, including rituals and sacrifices. Knowledge transmission followed the traditional guru-shishya tradition, where tribal healers learned from experienced healers orally, without written texts. Certification was valued as a way to gain public trust, and NGOs and federations played pivotal roles in advocating for traditional healing practices. Successful integration into mainstream healthcare required collaboration, coordination, and mutual respect between traditional and modern healthcare providers. Despite deep-rooted connections with their own communities, traditional healers face several common challenges in their practice such as Stigmatization and lack of recognition, Limited resources and infrastructure, Lack of formal training and certification, Legal and regulatory challenges, Ethical and legal dilemmas, and economic challenges. In conclusion, the landscape analysis shed light on the diverse healing traditions within tribal communities, emphasizing the importance of preserving and respecting these practices to safeguard cultural heritage and wisdom. Integrating traditional healing into comprehensive healthcare systems can enhance inclusivity and provide holistic care for tribal populations.

Efficient and accurate exponential SAV algorithms with relaxation for dissipative system

In this paper, we construct two kinds of exponential SAV approach with relaxation (R-ESAV) for dissipative system. The constructed schemes are linear and unconditionally energy stable. They can guarantee the positive property of SAV without any assumption compared with R-SAV and R-GSAV approaches, preserve all the advantages of the ESAV approach and satisfy dissipation law with respect to a modified energy which is directly related to the original free energy. We also give the rigorous consistency estimates of the constructed schemes for the L2 gradient flows. Moreover, the second version of R-ESAV approach is easy to construct high-order BDFk schemes. Especially for Navier–Stokes equations, we construct two kinds of novel schemes based on the R-ESAV method. Finally, ample numerical examples are presented to exhibit that the proposed approaches are accurate and effective.

Singlet-triplet dephasing in radical pairs in avian cryptochromes leads to time-dependent magnetic field effects.

Cryptochrome 4a (Cry4a) has been proposed as the sensor at the heart of the magnetic compass in migratory songbirds. Blue-light excitation of this protein produces magnetically sensitive flavin-tryptophan radical pairs whose properties suggest that Cry4a could indeed be suitable as a magnetoreceptor. Here, we use cavity ring-down spectroscopy to measure magnetic field effects on the kinetics of these radical pairs in modified Cry4a proteins from the migratory European robin and from nonmigratory pigeon and chicken. B1/2, a parameter that characterizes the magnetic field-dependence of the reactions, was found to be larger than expected on the basis of hyperfine interactions and to increase with the delay between pump and probe laser pulses. Semiclassical spin dynamics simulations show that this behavior is consistent with a singlet-triplet dephasing (STD) relaxation mechanism. Analysis of the experimental data gives dephasing rate constants, rSTD, in the range 3-6 × 107s-1. A simple "toy" model due to Maeda, Miura, and Arai [Mol. Phys. 104, 1779-1788 (2006)] is used to shed light on the origin of the time-dependence and the nature of the STD mechanism. Under the conditions of the experiments, STD results in an exponential approach to spin equilibrium at a rate considerably slower than rSTD. We attribute the loss of singlet-triplet coherence to electron hopping between the second and third tryptophans of the electron transfer chain and comment on whether this process could explain differences in the magnetic sensitivity of robin, chicken, and pigeon Cry4a's.