Quadratic Energy Research Articles

Optimal containment control for multi‐agent systems using fast adaptive dynamic programming

AbstractIn this paper, an innovative adaptive dynamic programming (ADP) algorithm with fast convergence speed is designed for the optimal containment control problem of discrete‐time linear multi‐agent systems. Precisely, a quadratic input energy cost function, including local containment error information and actuator information in the neighborhood, is designed for each follower. Solving the stationary condition of the cost function, the optimal containment controllers are obtained. Traditional ADP methods use actor–critic neural networks to approximate optimal costs and control strategies, it is time‐consuming to solve large‐scale multi‐agent problems due to the computational complexity of neural networks. In order to seek faster convergence speed of optimal containment control without knowing the model information, the fast ADP algorithm framework is designed, it is proved theoretically that the convergence speed is determined by some configurable parameters, and the whale optimization algorithm is employed to globally optimize the parameters of given spaces to derive the optimal configuration. Finally, numerical simulation results are given to verify the effectiveness of the designed algorithm.

The feature extraction method based on quadratic wavelet packet energy entropy and t-SNE for bearing fault diagnosis

The feature extraction method based on quadratic wavelet packet energy entropy and t-SNE for bearing fault diagnosis

Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity

Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymptotic description in the limit of a large number of cells. Starting from a bar and hinge model for the elastic energy of a generic four parallelogram panel origami pattern, we derive a complete set of geometric compatibility conditions identifying the pattern’s soft modes in this limit. The compatibility equations form a system of partial differential equations constraining the actuation of the origami’s creases (a scalar angle field) and the relative rotations of its unit cells (a pair of skew tensor fields). We show that every solution of the compatibility equations is the limit of a sequence of soft modes — origami deformations with finite bending energy and negligible stretching. Using these sequences, we derive a plate-like theory for parallelogram origami patterns with an explicit coarse-grained quadratic energy depending on the gradient of the crease-actuation and the relative rotations of the cells. Finally, we illustrate our theory in the context of two well-known origami designs: the Miura and Eggbox patterns. Though these patterns are distinguished in their anticlastic and synclastic bending responses, they show a universal twisting response. General soft modes captured by our theory involve a rich nonlinear interplay between actuation, bending and twisting, determined by the underlying crease geometry.

Confinement energy landscape classification reveals membrane receptor nano-organization mechanisms

The cell membrane organization has an essential functional role through the control of membrane receptor confinement in micro- or nanodomains. Several mechanisms have been proposed to account for these properties, although some features have remained controversial, notably the nature, size, and stability of cholesterol- and sphingolipid-rich domains or lipid rafts. Here, we probed the effective energy landscape acting on single-nanoparticle-labeled membrane receptors confined in raft nanodomains— epidermal growth factor receptor (EGFR), Clostridium perfringens ε-toxin receptor (CPεTR), and Clostridium septicum α-toxin receptor (CSαTR)—and compared it with hop-diffusing transferrin receptors. By establishing a new analysis pipeline combining Bayesian inference, decision trees, and clustering approaches, we systematically classified single-protein trajectories according to the type of effective confining energy landscape. This revealed the existence of only two distinct organization modalities: confinement in a quadratic energy landscape for EGFR, CPεTR, and CSαTR (A), and free diffusion in confinement domains resulting from the steric hindrance due to F-actin barriers for transferrin receptor (B).The further characterization of effective confinement energy landscapes by Bayesian inference revealed the role of interactions with the domain environment in cholesterol- and sphingolipid-rich domains with (EGFR) or without (CPεTR and CSαTR) interactions with F-actin to regulate the confinement energy depth. These two distinct mechanisms result in the same organization type (A). We revealed that the apparent domain sizes for these receptor trajectories resulted from Brownian exploration of the energy landscape in a steady-state-like regime at a common effective temperature, independently of the underlying molecular mechanisms. These results highlight that confinement domains may be adequately described as interaction hotspots rather than rafts with abrupt domain boundaries. Altogether, these results support a new model for functional receptor confinement in membrane nanodomains and pave the way to the constitution of an atlas of membrane protein organization.

Influence of quadratic thermal radiation and activation energy impacts over oblique stagnation point hybrid nanofluid flow across a cylinder

Quadratic thermal radiation is a fundamental term within the field of radiative heat transfer, which pertains to the interaction of thermal radiation. It encompasses a quadratic correlation between temperature and radiative qualities. Although linear thermal radiation is more prevalent in numerous everyday applications, non-linear thermal radiation is important in some situations, particularly where a more precise representation of the radiative transfer of heat is required. The phenomenon assumes a crucial function in some contexts that need enhanced accuracy in modeling radiative heat transfer. In view of this, the present investigation is carried out to examine the hybrid nanofluid flow across a cylinder under the influence of quadratic, nonlinear and linear thermal radiation and activation energy. The governing system of nonlinear differential equations is transformed into a system of ordinary differential equations via similarity transformations. The current study presents the results utilizing the shooting and Runge-Kutta Fehlberg 45 numerical scheme. The outcomes show that the curvature constraint will improve all three profiles while solid fraction decreases velocity and raises the other two profiles. Quadratic thermal radiation shows less temperature distribution, followed by linear and non-linear thermal radiation cases. The rate of thermal distribution improves 0.60 % for linear thermal radiation case, 0.52 % for nonlinear thermal radiation case and 0.656 % for quadratic thermal radiation case from hybrid nanofluid to nanofluid. Further, the rate of mass transfer shows 0.068 % improvement for from hybrid nanofluid to nanofluid. The results provide useful insights that may be used to enhance system efficiency across various applications, including but not limited to the mechanics of fluids, chemical technology, and thermal administration.

On energy complexity of fully-connected layers

The massive increase in the size of deep neural networks (DNNs) is accompanied by a significant increase in energy consumption of their hardware implementations which is critical for their widespread deployment in low-power mobile devices. In our previous work, an abstract hardware-independent model of energy complexity for convolutional neural networks (CNNs) has been proposed and experimentally validated. Based on this model, we provide a theoretical analysis of energy complexity related to the computation of a fully-connected layer when its inputs, outputs, and weights are transferred between two kinds of memories (DRAM and Buffer). First, we establish a general lower bound on this energy complexity. Then, we present two dataflows and calculate their energy costs to achieve the corresponding upper bounds. In the case of a partitioned Buffer, we prove by the weak duality theorem from linear programming that the lower and upper bounds coincide up to an additive constant, and therefore establish the optimal energy complexity. Finally, the asymptotically optimal quadratic energy complexity of fully-connected layers is experimentally validated by estimating their energy consumption on the Simba and Eyeriss hardware.

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull.

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

Magnetic quadratic nodal lines in half-metallic anode material TiF3: A first-principles study

It is anticipated that nodal line materials may demonstrate unique physical phenomena. The traditional nodal line materials have a linear energy distribution surrounding them. A recent prediction is that systems may similarly stabilize nodal lines with a quadratic or cubic energy dispersion. This work focuses on a half-metal anode material, TiF3, which has already been predicted to host stable ferromagnetism and half-metallicity under Li insertion. Using first-principles calculation, we predicted for the first time that TiF3, a ferromagnetic material, has completely spin-polarized quadratic nodal lines along the Γ-X path. The half-metallic state and the spin-polarized quadratic nodal lines are robust to uniform strains (from −3 to +3 %). TiF3 can be regarded as a promising platform for deepening our comprehension of magnetic quadratic nodal lines in half-metals.

Planar quartic G2 Hermite interpolation for curve modeling

We study planar quartic G2 Hermite interpolation, that is, a quartic polynomial curve interpolating two planar data points along with the associated tangent directions and curvatures. When the two specified tangent directions are non-parallel, a quartic Bézier curve interpolating such G2 data is constructed using two geometrically meaningful shape parameters which denote the magnitudes of end tangent vectors. We then determine the two parameters by minimizing a quadratic energy functional or curvature variation energy. When the two specified tangent directions are parallel, a quartic G2 interpolating curve exists only when an additional condition on G2 data is satisfied, and we propose a modified optimization approach. Finally, we demonstrate the achievable quality with a range of examples and the application to curve modeling, and it allows to locally create G2 smooth complex shapes. Compared with the existing quartic interpolation scheme, our method can generate more satisfactory results in terms of approximation accuracy and curvature profiles.

Quadratic energy–momentum squared gravity: Constraints from big bang nucleosynthesis

In this work, we extend the standard cosmological model within the quadratic energy–momentum squared gravity (qEMSG) framework, introducing a nonminimal interaction between the usual material field (Tμν) and its accompanying partner field (qEMSF, TμνqEMSF), defined by f(T2)=αT2 with T2=TμνTμν. Adopting an analytical approach within the qEMSG framework, we present a comprehensive exploration of Big Bang Nucleosynthesis (BBN) dynamics. Our analysis selects the radiation-dominated universe solution compatible with the standard cosmological model limit as α→0 and reveals that qEMSF interaction model can modify the radiation energy density’s evolution, potentially altering neutron–proton interconversion rates and consequently affecting 4He abundance in various ways. By explicitly defining modifications to the predicted primordial 4He mass fraction, Yp, we establish the most stringent cosmological constraints on the parameter α based on recent measurements of Yp: (−8.81≤α≤8.14)×10−27eV−4 (68% CL) from Aver et al.’s primordial 4He abundance measurements, aligning with α=0. Additionally, (3.48≤α≤4.43)×10−27eV−4 (68% CL) from Fields et al.’s estimates, utilizing the Planck-CMB estimated baryon density within the standard cosmological model framework, diverges from α=0, thereby lending support to the qEMSF interaction model. The study also highlights the bidirectional nature of energy–momentum/entropy transfer in qEMSF interaction model, depending on the sign of α. The implications of qEMSF in the presence of additional relativistic relics are also explored, showcasing the model’s potential to accommodate deviations from standard cosmology and the Standard Model of particle physics.

Construction of Bézier surfaces with minimal quadratic energy for given diagonal curves

Diagonal curve is one of the most important shape measurements of tensor-product Bézier surfaces. An approach to construct Bézier surfaces with energy-minimizing from two prescribed diagonal curves is presented in this paper. Firstly, a general second order functional energy is formulated with several parameters. This functional includes many common functionals as special cases, such as the Dirichlet energy, the biharmonic functional and the quasi-harmonic functional etc. Secondly, the necessary and sufficient conditions for tensor-product Bézier surface with minimal energy from prescribed diagonal curves are derived. Besides prescribing the diagonal curves, other related problems are considered, those where boundary curves are also prescribed. Finally, the effectiveness of the proposed method is illustrated by several surface modeling examples.

Bilevel Quadratic Programming-Based Stability and Energy Saving Control for Electric Vehicles Using Neurodynamic Optimization

Stability and energy saving are essential issues for traditional and autonomous vehicles and can be ensured through optimization and control of steering, braking, and torque distribution in electric motors. While these three control mechanisms can be optimized separately using two-stage sequential optimization, the results are often sub-optimal. As such, this study proposes simultaneous optimization and control of all three control units for the first time through Bilevel Quadratic Programming (BQP) with neurodynamic optimization. First, a BQP technique is developed by assuming the lower optimization problem to be a feasible region for the upper optimization problem. Second, the upper and lower optimization problems are integrated into a QP task to achieve simultaneous optimization and control by removing separate steps required for two-stage sequential optimization. As the formulated QP problem is more generalized, including an irreversible positive semi-definite hessian matrix and a switching subsystem, a novel neurodynamic optimization with a unique 2-norm energy function is established. It is then applied to solve the generalized BQP problem with high computational efficiency. Finally, hardware-in-the-loop experimental results confirmed the real-time effectiveness of the proposed control technique which decreased the optimization time by 43.3%, and improved control performance while reducing the braking and motor torque required by 54.6% and 33.3% respectively (compared with existing techniques).

Optimal Control of Temporal Networks With Variable Input and Node-Source Connection.

Many networked systems built upon real-life physical or social interactions have time-varying connections among individual units, where the temporal changes in connectivity and/or interaction strength lead to complicated dynamics. The temporal network model was proposed in the form of controlled linear dynamical systems acting in an ordered sequence of time intervals. One of the core challenges in network science is the control of networks and the optimization of the control strategy. However, most canonical frameworks for solving optimal control problems were established for static networks featuring constant topology. New theories and techniques are yet to be developed for the temporal networks, with an important case being that the input and the source-node connection are both variables. In this work, by formulating a quadratic energy cost without solving the Riccati differential equation, we show that the control effort can be reduced substantially by improving either the system trajectories or the input matrices. The two approaches are further combined in a coordinate descent framework, integrating linearly constrained quadratic programming, and a projected gradient descent method. Taken together, the results underline the potential of temporal networks as energy-efficient control systems and present strategies to improve the control input. Moreover, the proposed algorithms can serve as a starting point for future engineering of real-world temporal networks.

Towards hand grip force assessment by using EMG estimators

The purpose of this study was to propose a method to assess individual regression (calibration) curves to establish a relationship between an isometric grip force and surface electromyography (EMG) estimator. In this study 18 healthy volunteers (12 male (23.0 ± 2.0 years) and 6 female (23.2 ± 0.7 years)) had been examined. Ten EMG estimators (mean absolute value, root mean square, entropy, energy, turns per second, mean of zero crossings, median power frequency, mean power frequency, and Hilbert transforms), two EMG locations (brachioradialis and flexor digitorum superficialis) and five types of regression curves (linear, exponential, power, logarithm, and quadratic polynomial) have been tested. Using a quadratic polynomial regression curve and energy EMG estimator of the flexor digitorum superficialis muscle, it was obtained the lowest dispersity of EMG estimator and the most accurate prediction of grip isometric force among all tested EMG estimators.

Entropy optimization and stability analysis in flow of quadratic radiative Ag−MgO/water hybrid micropolar nanofluid over an exponentially contracting permeable Riga surface

ABSTRACT Driven by the significant thermal relevance of low-conductivity electrically active fluids and their impact on controlling flows across multiple industrial and engineering domains, this study aims to thoroughly investigate the primary behavior of electro-magneto-non-Newtonian micropolar A g − M g O / H 2 O hybridized nanofluid, specifically focusing on its flow dynamics and heat transfer characteristics over an exponentially contracting porous Riga surface. The Riga surface, an exceptional electromagnetic sensor surface, holds potential applications in micro-coolers, submarines, and nuclear reactor heat management systems. These findings hold significant relevance due to the prevalent use of micropolar hybridized nanofluids in cooling minute electronic components such as microchips and associated equipment. Our innovative objective is to emphasize the influence of an electromagnetic Riga plate in conjunction with micropolar characteristics, quadratic thermal radiant energy, convective conditions, and velocity slip at the boundary on various key parameters. These parameters include the coefficient of shear stress, coefficient of couple-stress, heat transfer factor (Nusselt number), entropy generation, velocity distribution, micro-rotation or angular velocity, and temperature profiles. We successfully tackled the highly intricate coupled partial differential equations by employing numerical techniques within the MATLAB programming platform. Specifically, we utilized a fourth-order method known as bvp4c to address the challenging boundary value problem. The outcomes revealed the existence of dual solutions characterized by a stable upper solution branch and an unstable lower solution branch within the region of the contracting sheet. Notably, this observation occurred under specific conditions related to the mass suction parameter. The identification of critical values in cases with dual solutions prompted a subsequent stability analysis to discern the nature and characteristics of these solutions. Two distinct solutions have been identified for λ S < λ , reaching termination at λ = λ S within the contracting region. Notably, the first solution yields a positive minimum eigenvalue ( β 1 > 0 ), indicating its stability, while the second solution results in a nonpositive eigenvalue ( β 1 < 0 ), implying instability. Graphical representations illustrate a substantial enhancement in nanofluid temperature for both solution branches, notably influenced by the quadratic thermal radiating parameter, Eckert number, and Biot number. Moreover, the magnetic interaction number and velocity slip parameter notably affect nanofluid motion within the first solution branch. Interestingly, it has been observed that the shear stress and couple stress coefficients exhibit an upward trend with increasing suction value. However, the heat transfer factor (Nusselt number) might decrease in the case of a stable solution. This research direction aims to optimize nanofluid compositions, aiming to minimize entropy generation while maximizing desired thermal properties. Such endeavors are crucial steps towards fostering more efficient and sustainable industrial practices, aligning with the overarching objectives of enhancing energy utilization and promoting industrial growth.

Edit propagation via color palettes

The ability to ease operation and real-time feedback to image editing has attracted increasing attention in our everyday lives. Existing edit propagation approaches typically formulate the color editing task as a quadratic energy optimization problem, which is computationally expensive and requires a lot of user interactions. To address this problem, in this paper, we propose a novel edit propagation method based on color palette. We first extract a color palette from the input image, and then calculate the mixing weights of the image pixels with respect to the extracted palette. Finally, we solve for an edited palette according to user edits, to propagate local edits to the whole image. Our main contributions include formulating the edit propagation as a palette-based optimization problem that can be solved efficiently, and requiring only fewer user interactions than existing methods. We have demonstrated our method for color editing on a wide range of examples. Compared to existing methods, our approach is more efficient and friendly for novice users due to its ease of interaction.

A steel joint for driven precast concrete geothermal energy pile foundations

This invention describes a steel joint used for connecting two precast concrete driven energy pile (DEP) segments which is known as DEP joint. Precast concrete DEPs are cast in segments with a maximum length of 12 m at a concrete factory. DEPs are typically driven into the ground until bedrock; hence, in places where the bedrock is deeper than 12 m, two or more segments must be connected using a joint to produce longer energy piles. DEPs have not been frequently used because no suitable joint existed that could maintain structural integrity and provide leak-proof coupling between the pipes at the joint interface. The present invention addresses this problem by designing a steel joint that can meet the structural and hydraulic requirements of a suitable steel joint for DEPs. Each quadratic concrete energy pile segment is prefabricated in a concrete factory, where the heat transfer pipes are embedded inside the steel cage of each segment. The steel DEP joint is installed at one or both ends of each concrete segment, and has two or four sidewall channels, depending upon its size. Heat transfer pipes are coupled between every two segments, inside the sidewall channels, while the energy piles are installed at a construction site. The sidewall channels are protected using steel shielding plates that are riveted to the joint so that the pipes and the coupling inside the sidewall channels are protected against harsh frictions during the installation of the DEPs in the ground. The steel joint facilitates the installation of longer precast concrete energy piles up to the bedrock depth, especially in sites where the bedrock is deeper than a single segment length. The main advantages of precast concrete energy piles compared to cast-in-place piles are that they enable better quality control and quality assurance, as well as being easier, faster, and cheaper to install. The invented DEP joint has passed structural integrity tests as required according to the BS EN 12794 standard, and also passed hydraulic pressure tests according to the ASTM F2164 – 21; hence, it is certified to be used in construction projects. We are now looking for potential licensees to start manufacturing the joints and using them in the energy pile industry.

Optimization of RSM and sensitivity analysis in MHD ternary nanofluid flow between parallel plates with quadratic radiation and activation energy

Optimization of RSM and sensitivity analysis in MHD ternary nanofluid flow between parallel plates with quadratic radiation and activation energy

An extended quadratic auxiliary variable method for the singular Lennard-Jones droplet liquid film model

In this letter, we present an extended quadratic auxiliary variable method for a droplet liquid film model characterized by the singular Lennard-Jones potential. This innovative approach begins with the introduction of three new auxiliary variables, each satisfying a quadratic equation, with the primary objective of reformulating the original model into an equivalent system. The reformulated system exhibits remarkable properties, including the preservation of three quadratic invariants and a quadratic energy dissipation law, where these auxiliary variables satisfy consistent initial conditions. To solve it numerically, we employ the implicit midpoint method in time and the central finite difference scheme in space to produce a second-order fully discrete scheme for the original model. Under consistent initial conditions, our proposed scheme is rigorously proved to preserve the original energy dissipation law at the fully discrete level. Numerical experiments showcase the scheme’s accuracy and effectiveness. It is noteworthy that the quadratic auxiliary variable method is extended to gradient flow systems featuring rational energy functionals.

High-order Lagrange multiplier method for the coupled Klein-Gordon-Schrödinger system

In this work, a novel class of high-order energy-preserving algorithms are developed for simulating the coupled Klein-Gordon-Schrödinger equations. We introduce a Lagrange multiplier approach and derive a new system which warrants exactly the original total energy, instead of the modified quadratic energy in the previous energy quadratization approach. The Lagrange system is then reformulated equivalently into an optimization problem subject to PDE constraints. We discretize the optimization system by applying the Gauss collocation method together with the prediction-correction technique in time and the sine pseudo-spectral method in space, which leads to a family of fully discrete high-order energy-preserving schemes. In the numerical experiments, we compare this method with other previous methods and verify the high accuracy as well as its ability to maintain the original energy at each time layer. The feasibility and validity of new method are also witnessed for the KGS model in the nonrelativistic limit regime. Additionally, enlightened by this seminal idea, another type of high-order numerical algorithms conserving two invariants of mass and energy are also presented and relevant experimental results are listed to verify the power of the suggested method.