Search Results (16)

In this research, we establish a precise correspondence between the theory of logarithmic connections on principal G-bundles over compact Riemann surfaces and the geometric formulation of control systems on curved manifolds, providing a novel differential–geometric framework for analyzing optimal control problems with non-holonomic constraints. By characterizing control systems through the geometric structure of flat connections with logarithmic singularities at marked points, we demonstrate that optimal trajectories correspond precisely to horizontal lifts with respect to the connection. These horizontal lifts project onto geodesics on the punctured surface, which is equipped with a Riemannian metric uniquely determined by the monodromy representation around the singularities. The main geometric result proves that the isomonodromic deformation condition translates into a compatibility condition for the control system. This condition preserves the conjugacy classes of monodromy transformations under variations of the marked points, and ensures the existence and uniqueness of optimal trajectories satisfying prescribed boundary conditions. Furthermore, we analyze systems with non-holonomic constraints by relating the constraint distribution to the kernel of the connection form, showing how the degree of non-holonomy can be measured through the failure of integrability of the associated horizontal distribution on the principal bundle. As an application, we provide computational implementations for $\mathrm{SL}(2,\mathbb{C})$ connections over hyperbolic Riemann surfaces with genus $g\ge 2$, explicitly constructing the monodromy-induced metric via the Poincaré uniformization theorem and deriving closed-form expressions for optimal control strategies that exhibit robust performance characteristics under perturbations of initial conditions and system parameters. Full article

Due to climate change, the electric vehicle (EV) industry is rapidly growing and drawing researchers interest. Driving conditions like mountainous roads, slick surfaces, and rough terrains illuminate the vehicles inherent nonlinearities. Under such scenarios, the behavior of power sources (fuel cell, battery, and super-capacitor), power processing units (converters), and power consuming units (traction motors) deviates from nominal operation. The increasing demand for FCHEVs necessitates control systems capable of handling nonlinear dynamics, while ensuring robust, precise energy distribution among fuel cells, batteries, and super-capacitors. This paper presents a DSMC strategy enhanced with Robust Uniform Exact Differentiators for FCHEV energy management. To optimally tune DSMC parameters, reduce chattering, and address the limitations of conventional methods, a hybrid metaheuristic framework is proposed. This framework integrates moth flame optimization (MFO) with the gravitational search algorithm (GSA) and Fractal Heritage Evolution, implemented through three spiral-based variants: MFOGSAPSO-A (Archimedean), MFOGSAPSO-H (Hyperbolic), and MFOGSAPSO-L (Logarithmic). Control laws are optimized using the Integral of Time-weighted Absolute Error (ITAE) criterion. Among the variants, MFOGSAPSO-L shows the best overall performance with the lowest ITAE for the fuel cell (56.38), battery (57.48), super-capacitor (62.83), and DC bus voltage (4741.60). MFOGSAPSO-A offers the most accurate transient response with minimum RMSE and MAE FC (0.005712, 0.000602), battery (0.004879, 0.000488), SC (0.002145, 0.000623), DC voltage (0.232815, 0.058991), and speed (0.030990, 0.010998)—outperforming MFOGSAPSO, GSA, and PSO. MFOGSAPSO-L further reduces the ITAE for fuel cell tracking by up to 29% over GSA and improves control smoothness. PSO performs moderately but lags under transient conditions. Simulation results conducted under EUDC validate the effectiveness of the MFOGSAPSO-based DSMC framework, confirming its superior tracking, faster convergence, and stable voltage control under transients making it a robust and high-performance solution for FCHEV. Full article

Conventional integer-order models fail to adequately capture non-local memory effects and constrained nonlinear interactions in emotional dynamics. To address these limitations, we propose a coupled framework that integrates Caputo fractional derivatives with hyperbolic tangent–based interaction functions. The fractional-order term quantifies power-law memory decay in affective states, while the nonlinear component regulates connection strength through emotional difference thresholds. Mathematical analysis establishes the existence and uniqueness of solutions with continuous dependence on initial conditions and proves the local asymptotic stability of network equilibria ($W_{ij}^{*}={\displaystyle \frac{1}{\delta }}{\sec \mathrm{h}}^2(\parallel {\mathrm{E}}_i-{\mathrm{E}}_j\parallel )$, e.g., $W^{*}\approx 1.40$ under typical parameters $\eta =0.5$, $\delta =0.3$). We further derive closed-form expressions for the steady-state variance under stochastic perturbations ($\mathrm{Var}\left(W_{ij}\right)={\displaystyle \frac{{\sigma }_{\zeta }^2}{2\eta \delta }}$) and demonstrate a less than 6% deviation between simulated and theoretical values when ${\sigma }_{\zeta }=0.1$. Numerical experiments using the Euler–Maruyama method validate the convergence of connection weights toward the predicted equilibrium, reveal Gaussian features in the stationary distributions, and confirm power-law scaling between noise intensity and variance. The numerical accuracy of the fractional system is further verified through L1 discretization, with observed error convergence consistent with theoretical expectations for $\mu =0.5$. This framework advances the mechanistic understanding of co-evolutionary dynamics in emotion-modulated social networks, supporting applications in clinical intervention design, collective sentiment modeling, and psychophysiological coupling research. Full article

This paper introduces an innovative approach to address the distribution network reconfiguration (DNR) challenge, aiming to reduce power loss through an advanced hyperbolic tangent particle swarm optimization (HT-PSO) method. This approach is distinguished by the adoption of a novel hyperbolic tangent function, which effectively limits the rate of change values, offering a significant improvement over traditional sigmoid function-based methods. A key feature of this new approach is the integration of a tunable parameter, $\delta$, into the HT-PSO, enhancing the curve’s adaptability. The careful optimization of $\delta$ ensures superior control over the rate of change across the entire operational range. This enhanced control mechanism substantially improves the efficiency of the search and convergence processes in DNR. Comparative simulations conducted on 33- and 94-bus systems show an improvement in convergence, demonstrating a more exhaustive exploration of the search space than existing methods documented in the literature based on PSO and variations where functions are proposed for the rate of change of values. Full article

In future aviation surveillance, the demand for higher real-time updates for global flights can be met by deploying automatic dependent surveillance–broadcast (ADS-B) receivers on low Earth orbit satellites, capitalizing on their global coverage and terrain-independent capabilities for seamless monitoring. Specific emitter identification (SEI) leverages the distinctive features of ADS-B data. High data collection and annotation costs, along with limited dataset size, can lead to overfitting during training and low model recognition accuracy. Transfer learning, which does not require source and target domain data to share the same distribution, significantly reduces the sensitivity of traditional models to data volume and distribution. It can also address issues related to the incompleteness and inadequacy of communication emitter datasets. This paper proposes a distributed sensor system based on transfer learning to address the specific emitter identification. Firstly, signal fingerprint features are extracted using a bispectrum transform (BST) to train a convolutional neural network (CNN) preliminarily. Decision fusion is employed to tackle the challenges of the distributed system. Subsequently, a transfer learning strategy is employed, incorporating frozen model parameters, maximum mean discrepancy (MMD), and classification error measures to reduce the disparity between the target and source domains. A hyperbolic space module is introduced before the output layer to enhance the expressive capacity and data information extraction. After iterative training, the transfer learning model is obtained. Simulation results confirm that this method enhances model generalization, addresses the issue of slow convergence, and leads to improved training accuracy. Full article

The complexity measure for the distribution in space-time of a finite-velocity diffusion process is calculated. Numerical results are presented for the calculation of Fisher’s information, Shannon’s entropy, and the Cramér–Rao inequality, all of which are associated with a positively normalized solution to the telegrapher’s equation. In the framework of hyperbolic diffusion, the non-local Fisher’s information with the x-parameter is related to the local Fisher’s information with the t-parameter. A perturbation theory is presented to calculate Shannon’s entropy of the telegrapher’s equation at long times, as well as a toy model to describe the system as an attenuated wave in the ballistic regime (short times). Full article

We address a hyperbolic model for prey-sensitive predators interacting with purely diffusive prey. We adopt the Cattaneo formulation for describing the predators’ transport. Given the hyperbolicity, the long-lived short-wave patterns occur for sufficiently weak prey diffusivities. The main result is that the non-linear interplay of the short waves generically excites the slowly growing amplitude modulation for wide ranges of the model parameters. We have observed such a feature in the numerical experiments and support our conclusions with a short-wave asymptotic solution in the limit of vanishing prey diffusivity. Our reasoning relies on the so-called homogenized system that governs slow evolutions of the amplitudes of the short-wave parcels. It includes a term (called wind) which is absent in the original model and only comes from averaging over the short waves. It is the wind that (unlike any of the other terms!) is capable of exciting the instability and pumping the growth of solutions. There is quite a definite relationship between the predators’ transport coefficients to be held for getting rid of the wind. Interestingly, this relationship had been introduced in prior studies of small-scale mosaics in the spatial distributions of some real-life populations. Full article

In this paper, a novel mathematical—physical model of the generalized elasto-thermodiffusion (hole/electron interaction) waves in semiconductor materials is studied when the hyperbolic two-temperature theory in the two-dimensional (2D) deformation is taken into account. Shear (purely transverse) waves are dissociated from the remainder of the motion and remain unaffected by external fields. The coupled system of partial differential equations of the main interacting fields has been solved. Using the Laplace transform method, the governing equations of motion and heat conduction can be formulated in 2D. The hole charge carrier, displacement, thermal, and plasma boundary conditions are applied on the interface adjacent to the vacuum to obtain the basic physical quantities in the Laplace domain. The inversion of the Laplace transform with the numerical method is applied to obtain the complete solutions in the time domain for the main physical fields under investigation. The effects of thermoelastic, the phase-lag of the temperature gradient and the phase-lag of the heat flux, the hyperbolic two-temperature parameter, and comparing between silicon and germanium materials on the displacement component, carrier density, hole charge carrier, and temperature distribution have been discussed and obtained graphically. Full article

The distribution of stresses near holes is of great importance in fracture mechanics and material modeling. The present paper provides a general stress solution near a traction-free surface for an arbitrary piecewise linear yield criterion, assuming plane-strain conditions. The generalized method of moving coordinates is proven efficient in this case. In particular, the solution reduces to evaluating one ordinary integral. The boundary value problem solved is a Cauchy problem for a hyperbolic system of equations. Therefore, the stress solution in the plastic region is independent of other boundary conditions, though the occurrence of plastic yielding at a specific point is path-dependent. The general solution applies to calculating the stress field near an elliptic hole. It is shown that the parameter that controls the pressure-dependency of the yield criterion affects the stress field significantly. The aspect ratio is less significant as compared to that parameter. However, for a given material, the aspect ratio should also be considered to predict the stress field accurately, especially in the near vicinity of the hole. The solution reduces to an available solution for the pressure-independent yield criterion, which is a particular yield criterion of the considered class of yield criteria. Full article

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid is comprehensively analyzed by considering the substantial impact of thermal conductivity and thermal radiation consequences. The governing PDEs (partial differential equations) are transmuted into a nonlinear differential structure of coupled ODEs (ordinary differential equations) using a series of variable similarity transformations. Furthermore, these generated ODEs (ordinary differential equations) are numerically set using a novel revolutionary Runge-Kutta algorithm with a shooting approach constructed in a MATLAB script. In this regard, extensive comparison studies are carried out to validate the acquired numerical results. The interactions between the associated profiles and the relevant parameters are rationally explored and shown using graphs and tabular forms. The velocity distribution declined with improving Weissengberg number $We$ and power-law index m, while the reverse performance can be observed for temperature. As enhancement in Brownian motion, Thermophoretic and radiation parameters significantly rise in temperature distribution. The use of many different technological and industrial systems, including nano-bioconvective systems, nano-droplet evaporation, nano-ink jet printing, and microbial fuel cells, would benefit this research study. Full article

This work reports a numerical investigation of microcombustion in an undulate microchannel, using premixed hydrogen and air to understand the effect of the burner design on the flame in order to obtain stability of the flame. The simulations were performed for a fixed equivalence ratio and a hyperbolic temperature profile imposed at the microchannel walls in order to mimic the heat external losses occurred in experimental setups. Due to the complexity of the flow dynamics combined with the combustion behavior, the present study focuses on understanding the effect of the fuel inlet rate on the flame characteristics, keeping other parameters constant. The results presented stable flame structure regardless of the inlet velocity for this type of design, meaning that a significant reduction in the heat flux losses through the walls occurred, allowing the design of new simpler systems. The increase in inlet velocity increased the flame extension, with the flame being stretched along the microchannel. For higher velocities, flame separation was observed, with two detected different combustion zones, and the temperature profiles along the burner centerline presented a non-monotonic decrease due to the dynamics of the vortices observed in the convex regions of the undulated geometry walls. The geometry effects on the flame structure, flow field, thermal evolution and species distribution for different inlet velocities are reported and discussed. Full article

A method for studying the effect of impulse perturbation on the longitudinal oscillations of a homogeneous constant cross-section of the body and the elastic properties of a material which satisfies the essentially nonlinear law of elasticity has been developed. A mathematical model of the process is presented, which is an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of impulse perturbation on the oscillatory process. As for the boundary conditions considered in the work, they are classic of the first, second and third genera. The methodology is based on: the principle of oscillation frequency in nonlinear systems with many degrees of freedom and distributed parameters; basic provisions of asymptotic methods of nonlinear mechanics; the idea of using special periodic Ateb-functions to construct solutions of some classes of nonlinear differential equations; properties of completeness and orthonormality of functions that describe the forms of oscillations of undisturbed motion. In general, the above allowed to obtain relations that describe for the first approximation the defining parameters of the oscillations of an elastic body. Their peculiarity is that even for undisturbed motion, the natural frequency of oscillations depends on the amplitude, and therefore, under the action of a periodic (over time) pulse force on the elastic body, both resonant and nonresonant processes are possible in the latter. It, in contrast to an elastic body with linear or quasilinear elastic properties of the body is determined not only by its basic physical and mechanical properties, but also by the amplitude of oscillations. As a special case, the oscillations of the body under the action of a constant periodic momentum perturbation are considered. It is shown that for the nonresonant case for the first approximation it does not affect the laws of change of amplitude and frequency of the process. As for the resonant is the amplitude of origin through the main resonance significantly depends not only on the speed but also on the points of action of the pulsed perturbation. Moreover, the closer the point of application of the pulsed force to the middle of the elastic body under boundary conditions of the first kind is greater (for boundary conditions of the second kind closer to the end). Full article

In this paper, we consider a class of first-order hyperbolic distributed parameter systems. Our focus is on the design of a new class of model predictive control schemes using a quasi-Shannon wavelet basis. First, the first-order hyperbolic distributed parameter system is transformed into an equivalent system using collocation techniques for the approximation of spatial derivatives and Euler forward difference method for the approximation of the time component. Then, a model reduction method is applied to obtain a reduced-order system on which a nonlinear model predictive controller is designed through solving a nonlinear quadratic programming problem with input constraints. For illustration, the temperature control of a flow-control long-duct heating system is considered to be an example. A comparative simulation study is conducted to demonstrate the effectiveness of the proposed method. Full article

Empirical models could help us to understand the process of plant residue decomposition and nutrient release into the soil. The objective of this study was to determine an appropriate model to describe the decomposition of hairy vetch (Vicia villosa Roth) and cereal rye (Secale cereale L.) cover crop (CC) residue and nitrogen (N) release. Data pertaining to above and belowground CC residue mass loss and N release for up to 2633 cumulative decomposition degree days (112 d) after litterbag installation were obtained from two cropping system experiments, a 1-yr study conducted in 2015 and a 2-yr study during 2017 to 2018 in the humid subtropical environment of southern IL, USA. Six exponential and two hyperbolic models were fit to percent mass and N remaining data to find the one with minimum Akaike information criterion (AIC) and residual sum of squares. Modified three-parameter single exponential and two- or three-parameter hyperbolic models best met the assumed criteria of selection for above and belowground CC residue, respectively. Fitting a double exponential model to combined data for percent mass and N remaining identified two mass and N pools, a fast and a slow pool with different rate constants. A five-parameter double exponential with an asymptote met the preset criteria and passed all tests for normally distributed population, constant variance, and independence of residuals at α = 0.05 when fit to combined data of hairy vetch shoot mass and N remaining. However, a two-parameter hyperbolic and three-parameter asymptotic hyperbolic model provided the best fit to a combined data of cereal rye shoot mass and N remaining, respectively. Both hyperbolic decay models showed a good fit for belowground mass decomposition and N release for both CCs. Cereal rye had a poorer fit than hairy vetch for mass and N remaining of both above and belowground mass. The best-selected decay models can be used to estimate the decomposition and N release rates of hairy vetch and cereal rye above and belowground residue in a similar environment. Full article

Strong nonlinearity and the relevance of time-varying dynamic parameters in the maneuverable process of water-jet propulsion were major problems encountered in the prediction of variable acceleration dynamics characteristics. The relationships between the thrust and rotation speed of a screw mixed-flow pump, drag and submerged speed of water-jet propulsion were obtained from flume experiments and numerical calculations, based on which a dynamic model of pump-jet propulsion was established in this paper. As an initial condition, the numerical solution of the submerged speed with respect to time was inputted to computational fluid dynamics (CFD) for unsteady calculation based on a user-defined function (UDF). Thus, the relationships between the acceleration, drag, net thrust, propulsion torque and efficiency with respect to time were revealed. The results indicate that the relationship between the thrust and rotational speed of a water-jet propeller is a quadratic function, which agrees well with the experimental values. The variation of submerged speed with respect to time satisfies a hyperbolic tangent function distribution. The acceleration increases sharply at the beginning and then decreases gradually to zero, especially at high rotation speeds of the water-jet pump. The variations in drag and propulsion efficiency with respect to time coincide with the step response of a second-order system with critical damping. The method and results of this study can give a better understanding of the changes in dynamic parameters such as velocity, acceleration, thrust, and drag during the acceleration of a pump-jet submersible and helped to estimate the effects of pump performance on water-jet propulsion kinetic parameters. Full article