Universal Function Research Articles

Further investigation on the fusion of 6Li with 209Bi target at near-barrier energies

Abstract The complete and incomplete fusion cross sections for 6Li+209Bi were measured via the in-beam γ-ray method around the Coulomb barrier. The cross sections of (deuteron captured) incomplete fusion (ICF) products were re-quantified experimentally for this reaction system. The results reveal that the ICF cross section is equivalent to that of complete fusion (CF) above the Coulomb barrier and dominant near or below the barrier. A theoretical calculation based on the Continuum Discretized Coupled Channel (CDCC) method is performed for the aforementioned CF and ICF cross sections, and the result is consistent with the experimental ones. The universal fusion function (UFF) is also compared with the measured CF cross section with different barrier parameters, demonstrating that the CF suppression factor is quite sensitive to the choice of potential, which can reflect both dynamic and static effects of breakup on the fusion process.

Investigating the impact of the universal function of the nuclear proximity potential in heavy-ion fusion cross sections

The fusion barriers and cross sections of 15 colliding systems with 320 ≤ Z 1 Z 2 ≤ 1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism. To realize this goal, we select three versions of the phenomenological proximity potentials, including Prox. 77, Zhang 2013, and Guo 2013, to calculate the nucleus–nucleus potential. The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations, including couplings to the low-lying 2+ and 3− states in the target and projectile. The calculated results show that the universal functions of the Guo 2013 and Prox. 77 models provide the lowest and highest fusion barriers, respectively. In addition, it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones. The highest sensitivity to the mass number of the projectile belongs to the results of Prox. 77. A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations. Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model. For the heavier systems, the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.

Universal hypothesis of autocorrelation function from Krylov complexity

In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients {bn}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\{b_{n}\\}$\\end{document} computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by b1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$b_{1}$\\end{document}, different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from {bn}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\{b_{n}\\}$\\end{document} that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems.

Effective mass function of radio meteoroids as a modulating factor in determining atmospheric scale height

Abstract A long-standing problem in meteor science has been the persistent presence of bias in the measured value of atmospheric scale heights obtained from radio meteor echoes. A common practice of fitting a linear function for bias correction follows the assumption that the systematic bias is devoid of seasonal asymmetry. This would be true if the mass and the velocity distribution of meteoroids remain invariant, both spatially and temporally. But so far no such convincing evidence has been published. On the contrary, fundamental arguments suggest that an universal mass function of radio meteoroids is counter-intuitive. This parameter cannot remain invariant due to the intrinsic variability in the meteor response function resulting from the Earth’s motion on the plane of ecliptic. In this paper, we show that an inverse relation exists between the width of meteor height distribution, expressed in unit of atmospheric scale height, and the exponent of the mass function. The overall mean of this exponent for the Sodankylä radar is 1.91 ± 0.02, modulated by a seasonal variation from the mean of the order of ∼±0.1. The stated inverse relation is applied to correct for the effect of mass distribution on the height distribution. Allowing for variable mass correction effectively removes the nonlinear bias in the measured scale heights in the meteor ionisation region.

First-Principles Calculations of the Mechanical Properties of Doped Cu3P Alloys.

In the quest to enhance the mechanical properties of CuP alloys, particularly focusing on the Cu3P phase, this study introduces a comprehensive investigation into the effects of various alloying elements on the alloy's performance. In this paper, the first principle of density universal function theory and the projection-enhanced wave method under VASP 5.4.4 software are used to recalculate the lattice constants, evaluate the lattice stability, and explore the mechanical properties of selected doped elements such as In, Si, V, Al, Bi, Nb, Sc, Ta, Ti, Y and Zr, including shear, stiffness, compression, and plasticity. The investigation reveals that strategic doping with In and Si significantly enhances shear resistance and stiffness, while V addition notably augments compressive resistance. Furthermore, incorporating Al, Bi, Nb, Sc, Ta, Ti, V, Y, and Zr has substantially improved plasticity, indicating a broad spectrum of mechanical enhancement through precise alloying. Crucially, the validation of our computational models is demonstrated through hardness experiments on Si and Sn-doped specimens, corroborating the theoretical predictions. Additionally, a meticulous analysis of the states' density further confirms our computational approach's accuracy and reliability. This study highlights the potential of targeted alloying to tailor the mechanical properties of Cu3P alloys and establishes a robust theoretical framework for predicting the effects of doping in metallic alloys. The findings presented herein offer valuable insights and a novel perspective on material design and optimization, marking a significant stride toward developing advanced materials with customized mechanical properties.

Dynamic event-triggered adaptive tracking control for stochastic nonlinear systems with deferred time-varying constraints

This article investigates the problem of adaptive tracking control for stochastic nonlinear systems with deferred state constraints. The novel unified universal barrier function (UUBF) and deferred funnel error transformation are developed to handle various state constraints and adjust the tracking error more precisely, respectively. Multi-dimensional Taylor network (MTN) and dynamic event-triggered mechanism (DETM) are employed to design controller in the backstepping process, which can achieve full-state constraints and the tracking control after the preassigned time while conserving more communication resources. Finally, two simulation examples are presented to verify the effectiveness of the proposed control scheme.

Distributed Event-Triggered Algorithm Designs for Resource Allocation Problems via a Universal Scalar Function-Based Analysis.

In this article, we are concerned with distributed algorithm designs for resource allocation problems via event-triggered communication. The target is to search an optimal resource allocation scheme such that the summation of objective functions is minimized. Due to communication efficiency and privacy concerns, distributed algorithms with event-triggered communications are proposed in this article. The communication is only permitted or triggered if variation of gradient of the local objective function exceeds a threshold. By constructing a novel technical lemma and a universal scalar function, the convergence and linear convergence rates are established under some mild assumptions. Extensive numerical experiments on the IEEE 118-bus power system demonstrate that: Compared to the periodic algorithms, such as ADMM and Mirror-P-EXTRA, the proposed algorithms not only remarkably reduce the communication times but also have competitive convergence speed. The latter is striking that it implies there exist useless communications in the periodic algorithms that are censored by the proposed event-triggered strategy.

Fixed-Time Rigidity-Based Formation Maneuvering for Nonholonomic Multirobot Systems With Prescribed Performance.

This article presents rigidity-based formation maneuvering for a group of nonholonomic mobile robots subject to limited sensing capability, where the performance bounds are introduced to constrain the distance and angle errors. The time-varying and asymmetric performance constraints can prescribe the transient and steady-state performance of the closed-loop systems, which further specify collision avoidance and connectivity maintenance among neighboring robots and avoid the controller singularity issue. To satisfy the constraint requirements and fixed-time convergence, universal barrier Lyapunov functions are incorporated with control design such that angle errors are fixed-time stable and distance errors can converge to a small neighborhood around zero in fixed time. Under the proposed control protocol, all robots can track the desired time-varying velocity while generating and maintaining the predefined formation defined by a minimally and infinitesimally rigid graph. Simulation and experiment studies are carried out to illustrate the effectiveness of the proposed control protocol.

An indirect training approach for implicit constitutive modelling using recurrent neural networks and the virtual fields method

Accurate material description is crucial to achieve high-quality results in computational analysis software. Phenomenological constitutive laws generalize the material behaviour observed in simple mechanical tests. The resulting empirical expressions contain parameters that need to be calibrated through an inverse optimization process. Advancements in Digital Image Correlation (DIC) techniques have enabled the extraction of non-uniform multi-axial displacement fields, facilitating the development of heterogeneous mechanical specimens and unlocking access to richer material behaviour data. Despite these advancements, constitutive models are still limited by mathematical formulations and biases due to simplifying assumptions. Artificial Neural Networks (ANNs), as universal function approximators, could potentially drive a paradigm shift in the field. ANNs do not require explicit pre-formulations, hence avoiding the need for identifying unknown parameters. Moreover, ANNs are able to implicitly learn patterns purely from data, allowing to circumvent the biases induced by the simplifying assumptions of first-order principles. However, the training of ANNs for implicit constitutive modelling is not straightforward, given the impossibility of obtaining direct measurements of stress. This paper explores the integration of Recurrent Neural Networks (RNNs) with the Virtual Fields Method (VFM) for material modelling. This approach uses global force and displacement data to indirectly train the neural network, with the equilibrium being evaluated globally through the VFM loss function. The proposed method is (i) computationally efficient by not requiring Finite Element Analysis (FEA), (ii) compatible with both full-field measurements and numerically generated data, and (iii) able to handle experimental boundary conditions.

Scaling properties of the action in the Riemann-Liouville fractional standard map.

The Riemann-Liouville fractional standard map (RL-fSM) is a two-dimensional nonlinear map with memory given in action-angle variables (I,θ). The RL-fSM is parameterized by K and α∈(1,2], which control the strength of nonlinearity and the fractional order of the Riemann-Liouville derivative, respectively. In this work we present a scaling study of the average squared action 〈I^{2}〉 of the RL-fSM along strongly chaotic orbits, i.e., for K≫1. We observe two scenarios depending on the initial action I_{0}, I_{0}≪K or I_{0}≫K. However, we can show that 〈I^{2}〉/I_{0}^{2} is a universal function of the scaled discrete time nK^{2}/I_{0}^{2} (n being the nth iteration of the RL-fSM). In addition, we note that 〈I^{2}〉 is independent of α for K≫1. Analytical estimations support our numerical results.

Summing up perturbation series around superintegrable point

We work out explicit formulas for correlators in the Gaussian matrix model perturbed by a logarithmic potential, i.e. by inserting Miwa variables. In this paper, we concentrate on the example of a single Miwa variable. The ordinary Gaussian model is superintegrable, i.e. the average of the Schur functions SQ is an explicit function of the Young diagram Q. The question is what happens to this property after perturbation. We show that the entire perturbation series can be nicely summed up into a kind of Borel transform of a universal exponential function, while the dependence on R enters through a polynomial factor in front of this exponential. Moreover, these polynomials can be described explicitly through a single additional structure, which we call “truncation” of the Young diagram Q. It is unclear if one can call this an extended superintegrability, but at least it is a tremendously simple deformation of it. Moreover, the vanishing Gaussian correlators remain vanishing and, hence, are not deformed at all.

Learning Spatially Collaged Fourier Bases for Implicit Neural Representation

Existing approaches to Implicit Neural Representation (INR) can be interpreted as a global scene representation via a linear combination of Fourier bases of different frequencies. However, such universal basis functions can limit the representation capability in local regions where a specific component is unnecessary, resulting in unpleasant artifacts. To this end, we introduce a learnable spatial mask that effectively dispatches distinct Fourier bases into respective regions. This translates into collaging Fourier patches, thus enabling an accurate representation of complex signals. Comprehensive experiments demonstrate the superior reconstruction quality of the proposed approach over existing baselines across various INR tasks, including image fitting, video representation, and 3D shape representation. Our method outperforms all other baselines, improving the image fitting PSNR by over 3dB and 3D reconstruction to 98.81 IoU and 0.0011 Chamfer Distance.

Event-triggered prescribed-time tracking for uncertain nonlinear systems with unknown control gain and output constraints

This paper uses a prescribed-time event-triggered approach to explore the control of uncertain strict-feedback nonlinear systems with output constraints and an unknown time-varying control gain. The proposed method utilizes a universal barrier Lyapunov function (BLF) to ensure compliance with the output constraints. Furthermore, a technique known as congelation of variables is employed to handle the unknown time-varying control gain. Approximating the unknown dynamics using radial basis function neural network (RBFNN), a neural prescribed-time controller is designed based on the backstepping approach. Additionally, the event-triggered mechanism is employed to conserve computational and communication resources. With this scheme, all signals are guaranteed to converge to a compact set within the prescribed time frame. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithm.

Quantitative coarse graining of laminar fluid flow penetration in rough boundaries

The interaction between a fluid and a wall is described with a certain boundary condition for the fluid velocity at the wall. To understand how fluids behave near a rough wall in a completely laminar flow regime, the fluid velocity at every point on the rough surface may be provided. This approach requires detailed knowledge of, and likely depends strongly on the roughness. Another approach of modelling the boundary conditions of a rough wall is to coarse grain and extract a penetration depth over which on average the fluid penetrates into the roughness. In this work, we examine the impact of well-defined patterned surfaces on the fluid flow behaviour. We considered two extreme cases: one with horizontal ridges and another with vertical ridges on the wall and an intermediate case with ridges at an angle on the wall. We show that for a broad range of periodic roughness patterns and relative flow velocities, a universal penetration depth function can be obtained. We obtain these results with experiments and complementary numerical simulations. We evaluate how this penetration depth depends on the various roughness parameters such as ridge depth, ridge spacing and ridge angle. Our results present a novel approach to investigating wall roughness boundary conditions by considering the penetration depth δ that captures the spatially averaged behaviour of the decaying velocity profile between the asperities. We find that this penetration depth δ can be rescaled into a simple exponential master curve δ = δ∞(1 − e−kD/S) for horizontal ridges with varying depth D and spacing S. A similar variation of δ with D and S is observed for vertical ridges, but with a smaller magnitude δ∞, while for ridges at an angle, the penetration depth lies between the two extreme cases.

Observation of Subdiffusive Dynamic Scaling in a Driven and Disordered Bose Gas.

We explore the dynamics of a tuneable box-trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power-law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.

Trajectory Re-Planning and Tracking Control for a Tractor–Trailer Mobile Robot Subject to Multiple Constraints

Autonomous tractor–trailer robots possess a broad spectrum of applications but pose significant challenges in control due to their nonlinear and underactuated dynamics. Unlike the tractor, the motion of the trailer cannot be directly actuated, which often results in a deviation from the intended path. In this study, we introduce a novel method for generating and following trajectories that circumvent obstacles, tailored for a tractor–trailer robotic system constrained by multiple factors. Firstly, leveraging the state information of both the obstacles and the desired trajectory, we formulate an improved trajectory for obstacle avoidance using the nonlinear least squares method. Subsequently, we propose an innovative tracking controller that integrates a universal barrier function with a state transformation strategy. This amalgamation facilitates the accurate tracking of the prescribed trajectory. Our theoretical analysis substantiates that the proposed control methodology ensures exponential convergence of the line-of-sight (LOS) distance and angle tracking errors, while enhancing the transient performance. To validate the efficacy of our approach, we present a series of simulation results, which demonstrate the applicability of the developed control strategy in managing the complex dynamics of tractor–trailer robots.

Research on optimization method of evaporation duct prediction model based on particle swarm algorithm

The sea surface roughness parameterization and universal stability functions, as key components of the evaporation duct prediction models rooted in the Monin-Obukhov similarity theory, dictate the model performance which further impacts the efficiency and accuracy of offshore electromagnetic applications. In this paper, layered meteorological and hydrological observations are collected during two cruises and processed to obtain the reference modified refractivity profiles close to the sea surface, and then particle swarm algorithm is utilized to optimize the parameters of the sea surface roughness parameterization and universal stability functions. The results show that compared with the pre-optimization model, the prediction accuracy of the optimized model is improved by 5.09% and 8.12% under stable conditions, and by 9.97% and 31.51% under unstable conditions for observation dataset from each cruise, which proves the feasibility of the proposed method for evaporation duct prediction model optimization.

Cooperative Control for Stochastic Multiagent Systems With Deferred Dynamic Constraints via a Novel Universal Barrier Function Approach.

This article investigates the cooperative control problem for stochastic multiagent systems (MASs) with dynamic constraints. A new universal barrier function is proposed, which is applicable to many systems with different types of constraint functions, even unconstrained systems. Several mapping functions are constructed to constrain the state variables directly without feasibility conditions, and the tracking control is achieved for stochastic MASs with deferred full-state constraints under the backstepping framework. In order to regulate the tracking error more precisely, the funnel error transformation is improved and the deferred funnel controller is developed by introducing a preassigned finite-time function. Based on the deferred funnel controller, the tracking error can be maintained within the predetermined funnel in the preassigned time. The convergence time can be defined according to the actual requirements, and it is independent of the design controller parameters and initial conditions. Finally, some simulation results are given to demonstrate the effectiveness of the proposed control algorithm.

Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism

This paper focuses on online recorded-data-based composite adaptive fuzzy bipartite consensus control for uncertain fractional-order multiagent systems with interconnected terms and external disturbances by employing a switched-threshold-based event-triggered mechanism (ETM) under the backstepping structure. Fuzzy logic system is used as a universal function approximation to deal with function uncertainties that are not prone to model in the system. A new composite learning adaptive parameter design scheme that synthesizes both prediction error and tracking error is developed to enhance the tracking performance, where the prediction error is raised from the utilization of online recorded data and instantaneous data. A unique switched-threshold-based ETM is introduced, in which the information transmission between the sensor and the controller is imposed on one of the individuals. One merit of this work consists in that it can automatically and rapidly switch and adjust between the fixed threshold and relative threshold ETM according to the amplitude of input signals to balance the network resources and impede the occurrence of pulse phenomenon. In addition, it is theoretically proven that the proposed scheme can ensure that all internal signals of the closed-loop system are bounded and achieve local bipartite consistent errors through the fractional Lyapunov stability criterion. Finally, a numerical example is provided to confirm the feasibility of the proposed approach.

Random Matrix Statistics in Propagating Correlation Fronts of Fermions.

We theoretically study propagating correlation fronts in noninteracting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime, all the moments of dynamical fluctuations around the correlation fronts are described by the universal correlation functions of Gaussian orthogonal and symplectic random matrices at the soft edge. Our finding here sheds light on a hitherto unknown connection between random matrix theory and correlation propagation in quantum dynamics.