Terms Of Energy Function Research Articles

Exergy and dynamics analyses in centrifugal turbomachinery pressurized long-distance natural gas pipelines based on Hamiltonian model

Natural gas pipelines represent intricate systems comprising diverse components, which is crucial to industry, yet demanding substantial energy consumption. However, the nuanced energy and exergy transfer dynamics within these pipelines, particularly during dynamic processes, remain relatively unexplored. Given the distributed nature and complicated component coupling among pipeline elements, coolers, and compressors, traditional energy analysis tools face challenges in their application. In this study, we introduce a novel approach utilizing Hamiltonian formalism to establish an energy and exergy analysis framework for natural gas pipelines. Specifically, we develop Hamiltonian energy functions for various components, including pipes, centrifugal compressors, and coolers, accounting for dynamic mechanisms. Through comprehensive simulations covering static and dynamic scenarios, we elucidate energy and exergy transfer processes, leveraging Hamiltonian energy function terms. Our findings validate the efficacy of the proposed analysis framework in accurately characterizing energy transfer and dissipation processes. Furthermore, validation with field data demonstrates the capability of our method to online exhibit energy transfer features effectively.

Automatic generation of interpretable hyperelastic material models by symbolic regression

AbstractIn this article, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation for example into a finite element procedure is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney–Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied to the multi‐axial loading data set of vulcanized rubber. Finally, a data set for a temperature‐dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.

Reverse physically motivated frameworks for investigation of strain energy function in rubber-like elasticity

This paper introduces three innovative frameworks to obtain the strain energy function for rubber-like materials through an inverse approach. To this end, we inspire from the statistical background of physically motivated models to represent the strain energy function in terms of variables that correspond to the kinetics of a polymeric chain. We employ the micro-sphere concept to cast different structure-based models with unknown core functions or kernels and reveal them directly from experimental data. Accordingly, we use the basis spline (B-Spline) curve to represent these core functions and derive the macroscopic stress tensor based on the unknown control points associated with the B-Spline curves. Following this, we define a loss function to tie experimental data to these unknown control points, followed by a least-square error minimization technique that ultimately leads to a linear system of equations. In this way, we circumvent the nonlinear optimization in current structure-based models used for material parameter fitting that comes with the solution’s uncertainty. We also minimize simplifying hypotheses and bypass the unnecessary assumptions that have been influenced the accuracy of physical-based methods. Furthermore, one can integrate these functions with a high accuracy scheme over the micro-sphere, resulting in an integration-free model with competitive computational complexity to closed-form models. Finally, we validate the robustness of each framework in a challenging benchmark for three different polymeric materials. Considering the same dataset for the calibration of all models( which is uniaxial, pure shear, and equi-biaxial tests), the proposed frameworks outperform other well-known physical-based models in the literature in this challenging benchmark to the best of our knowledge ( we also show that the same performance is attainable by using only uniaxial and equi-biaxial tests ). Moreover, in the case of a limited dataset, we show that it is possible to apply prior knowledge regarding a material into one of the frameworks (RFN) to enhance the accuracy of predictions.

Dynamic and static response of a slightly compressible hyperelastic solid

The paper presents dynamic and static response of a slightly compressible hyperelastic solid. Material models under consideration are obtained by extending incompressible material models which are consistent second and third order approximation of existing stored energy function in terms of a deformation measure, namely MCMV and MCIZ. The problems of a uniaxial compression of a rod and a twisting column are solved using ABAQUS which is a powerful finite element program designed for general use in nonlinear problems. The models are defined with a help of user subroutine UHYPER. In the case of including dynamic effects, an implicit integration scheme available in the software is used. For the twisting column problem, results are compared against available in the ABAQUS library polynomial model where the volumetric stored energy function does not meet basic growth conditions. Experimental data on synthetic rubber neoprene published in the literature is utilized.

Adaptive Shape based Interactive Approach to Segmentation for Nodule in Lung CT Scans

In lung cancer diagnosis, growth of pulmonary nodule should be detected perfectly. Mostly watershed segmentation methods play a very important role in lung CT images to detect their growth. But this method detection will be ineffective in terms of energy function and speed as well. The proposed modified graph-cut technique is providing the good performing result in the speed and accuracy of the process than the conservative graph cut methods. Also, this research paper is proposed adaptive shape based interactive approach to segmentation for lung CT scan image and provide a more efficient. This proposed algorithm is proving that the energy function of the system is lesser than old methods. In this research paper, applying shape-based technique in segmentation technique has been proposed and proved for better accuracy with low energy function.

Axiomatization, Computability and Stability for Discrete Event Time Algorithms

This work proposes a formalization of discrete event time algorithms. A Church type thesis, its proof, and the notion of stability for discrete event time algorithms are presented. The Church thesis for discrete algorithms motivates us to consider the Church thesis for the case when we are dealing with discrete event time algorithms. The notions of discrete event time algorithm and discrete event time dynamical system are postulated to be equivalent. The stability concept for discrete event time algorithms is defined. The stability analysis presentation starts concentrating in discrete event time algorithms, i.e., discrete event time dynamical systems, whose Petri net model is described by difference equations, and continues considering Lyapunov energy function sin terms of the logical structures of the vocabulary. A stability analysis based on the reachability tree of the Petri net model is also discussed.

Form-finding of cable-strut structures with given cable forces and strut lengths

This paper presents a form-finding method for cable-strut structures with given cable forces and strut lengths. The topology of the structure, the internal force distribution of cables and the rest length of struts are given in advance. A total potential energy function in terms of nodal coordinates is derived according to the initial conditions. The equilibrium configuration satisfying the given initial conditions is essentially a stationary point of the energy function. An intermediate function is proposed and used to solve the stationary point problem. A configuration expected by the designer can be obtained when proper initial nodal coordinates are used. The effectiveness and practicability of the proposed method are verified by two typical examples.

Decay in chemotaxis systems with a logistic term

This paper is concerned with a general fully parabolic Keller-Segel system, defined in a convex bounded and smooth domain $Ω$ of $\mathbb{R}^N, $ for N∈{2, 3}, with coefficients depending on the chemical concentration, perturbed by a logistic source and endowed with homogeneous Neumann boundary conditions. For each space dimension, once a suitable energy function in terms of the solution is defined, we impose proper assumptions on the data and an exponential decay of such energies is established.

Function-refresh algorithms for determining the stored energy density of nonlinear elastic orthotropic materials directly from experimental data

The typical approach to hyperelasticity is to assume an analytical expression of the stored energy function in terms of invariants and some constants, named “material parameters”. From available experimental data, a different data-driven approach is to establish specific function dependencies such that the stored energy can be uniquely determined in a numerical, deterministic way, exactly capturing smooth experimental data curves. In this approach the functions are not restricted to an analytical form and the model does not employ material parameters. Whereas the overall ideas regarding the search for a numerical solution employing proper interpolation functions are common, the actual computational procedure depends on the assumed function dependencies from available experimental data and known material symmetries. For the case of orthotropic materials, it is possible to assume a strain energy decomposition in terms of logarithmic strains which guarantees consistency with the infinitesimal theory at all deformation levels. At the same time, this energy can be determined with a minimum amount of tests. In previous works we introduced algorithms which use a generalization of the Kearsley–Zapas inversion formula for orthotropy. This approach lacks the desired generality to account for different reduced forms and possible tests available to the analyst. In this work we use a simpler approach using function-refresh algorithms, which allows us to obtain the stored energy density of orthotropic materials in more general cases.

An optimal particle setup method with Centroidal Voronoi Particle dynamics

In this paper, we develop an optimal particle setup method for initial condition with Centroidal Voronoi Particle (CVP) dynamics, which combines the Centroidal Voronoi Tessellation (CVT) and Voronoi Particle (VP) concept. CVT optimizes the energy function in terms of compactness and consequently ensures the isotropy of particle distribution. The CVT configuration is computed by Lloyd’s algorithm, which decreases the energy function monotonically. A physics-motivated model equation with tailored equation of state (EOS) is employed to relax the Voronoi particle system such that the convergent equilibrium matches the target configuration. The resulting particle distribution approximates the given analytical profiles of spatially adaptive density, smoothing-length and mass distribution with high interpolation accuracy. The level-set method is introduced to describe arbitrarily complex geometries. A set of Smoothed Particle Hydrodynamics (SPH) simulations is computed to demonstrate the performances of the proposed method. Without parameter tuning, good performance is obtained for presented benchmarks implying its promising potential.

A non-ellipticity result, or the impossible taming of the logarithmic strain measure

Constitutive laws in terms of the logarithmic strain tensor logU, i.e. the principal matrix logarithm of the stretch tensor U=FTF corresponding to the deformation gradient F, have been a subject of interest in nonlinear elasticity theory for a long time. In particular, there have been multiple attempts to derive a viable constitutive law of nonlinear elasticity from an elastic energy potential which depends solely on the logarithmic strain measure ‖logU‖2, i.e. an energy function W:GL+(n)→R of the form (1)W(F)=Ψ(‖logU‖2)with a suitable function Ψ:[0,∞)→R, where ‖.‖ denotes the Frobenius matrix norm and GL+(n) is the group of invertible matrices with positive determinant.However, while such energy functions enjoy a number of favorable properties, we show that it is not possible to find a strictly monotone function Ψ such that W of the form (1) is Legendre–Hadamard elliptic.Similarly, we consider the related isochoric strain measure ‖devnlogU‖2, where devnlogU is the deviatoric part of logU. Although a polyconvex energy function in terms of this strain measure has recently been constructed in the planar case n=2, we show that for n≥3, no strictly monotone function Ψ:[0,∞)→R exists such that F↦Ψ(‖devnlogU‖2) is polyconvex or even rank-one convex. Moreover, a volumetric-isochorically decoupled energy of the form F↦Ψ(‖devnlogU‖2)+Wvol(detF) cannot be rank-one convex for any function Wvol:(0,∞)→R if Ψ is strictly monotone.

Transient Stability Enhancement of Power Grid With Integrated Wide Area Control of Wind Farms and Synchronous Generators

This paper presents a Wide Area Control (WAC) design to enhance the transient stability of Doubly Fed Induction Generators (DFIG) integrated power grid. The proposed WAC design is based on a nonlinear optimal control algorithm using Reinforcement Learning (RL) and Neural Networks (NNs), which optimizes the closed-loop performance of the wind integrated power grid through Approximate Dynamic Programming (ADP). The aim of the WAC is to estimate the global energy function of the system, independent of the contingency, and derive supplementary damping control to augment the excitation system of synchronous generators and local active and reactive power control of DFIG. The controller objective is evolved from transient energy function terms developed for synchronous generators and wind farms within the framework of a coupled oscillatory system. The theoretical results are verified by conducting simulation studies on the modified IEEE 68-bus system with three aggregated wind farms modeled in electromagnetic transient simulator test-bed. It has been shown that the method improves transient stability of the test system and damps the interarea oscillations faster, including the active and reactive power support from DFIG during grid transient conditions.

Enhancing power system transient stability using optimal unified power flow controller based on Lyapunov control strategy

This paper presents a new control strategy for an Optimal Uni ed Power Flow Controller (OUPFC) through a Lyapunov energy function in terms of local parameters to improve the transient stability of a power system. The OUPFC is a hybrid con guration of Flexible AC Transmission System (FACTS) devices, i.e. an arrangement of small-sized Uni ed Power Flow Controller (UPFC) and a full-scale Phase Shifting Transformer (PST).In this study, a new term of OUPFC's energy function and its injection model in a simpli ed structure preserving model is developed and implemented in a two-machine power system using MATLAB/Simpower. The ability of the OUPFC controller to enhance the transient stability is compared to that of UPFC. The results show that using the proposed control strategy for OUPFC leads to more abatement of the rst swing oscillations and enlargement of stability margin. It is concluded that compensation of UPFC's angle displacement maycome true using OUPFC with appropriate angles in proper locations. So, compared to UPFC, OUPFC enjoys another degree of freedom.

Internal Rotation of Methylcyclopropane and Related Molecules: Comparison of Experiment and Theory.

The internal rotation about the single bond connecting a cyclopropyl ring to a CH3, SiH3, GeH3, NH2, SH, or OH group was investigated. Both CCSD/cc-pVTZ and MP2/cc-pVTZ ab initio calculations were performed to predict the structures of these molecules and their internal rotation potential energy functions in terms of angles of rotation. The barriers to internal rotation for the CH3, SiH3, and GeH3 molecules from the calculations agree well with the experimental ones, within -11% to +1% for CCSD/cc-pVTZ and -4% to +9% for MP2/cc-pVTZ. Comparisons between theory and experiment were also performed for propylene oxide and propylene sulfide, and the agreements were very good. Theoretical calculations were performed to compute the internal rotation potential energy function for cyclopropanol, and these were used to guide the determination of a potential function based on experimental data. This molecule has two equivalent synclinal (gauche) conformers with an estimated barrier of 759 cm(-1) (9.1 kJ/mol) between them. The minima are at internal rotation angles of the OH group of 109° and 251°. The theoretical potential functions for cyclopropanethiol and cyclopropylamine were also calculated, and these agree reasonably well with previous experimental studies.

Probabilistic delay differential equation modeling of event-related potentials

“Dynamic causal models” (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach.

Constitutive Relation for Large Deformations of Fiber-Reinforced Rubberlike Materials with Different Response in Tension and Compression

ABSTRACT Fiber-reinforced rubberlike materials commonly used in tires undergo large deformations and exhibit different responses in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function in terms of the five invariants of the right Cauchy-Green strain tensor and account for different response in tension and compression along the fiber direction. The constitutive relation accounts for both material and geometric nonlinearities and incorporates effects of the fifth strain invariant, I5. It has been shown by Merodio and Ogden that in shear dominated deformations, I5 makes a significant contribution to the stress-strain curve. We have implemented the proposed constitutive relation in the commercial software, LS-DYNA. The numerical solutions of a few boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which part of the solution is assumed and unknowns in the presumed solution are found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. When test data become available, one can modify the form of the strain energy density and replace the proposed constitutive relation by the new one in LS-DYNA.

Automated cerebellar lobule segmentation with application to cerebellar structural analysis in cerebellar disease

The cerebellum plays an important role in both motor control and cognitive function. Cerebellar function is topographically organized and diseases that affect specific parts of the cerebellum are associated with specific patterns of symptoms. Accordingly, delineation and quantification of cerebellar sub-regions from magnetic resonance images are important in the study of cerebellar atrophy and associated functional losses. This paper describes an automated cerebellar lobule segmentation method based on a graph cut segmentation framework. Results from multi-atlas labeling and tissue classification contribute to the region terms in the graph cut energy function and boundary classification contributes to the boundary term in the energy function. A cerebellar parcellation is achieved by minimizing the energy function using the α-expansion technique. The proposed method was evaluated using a leave-one-out cross-validation on 15 subjects including both healthy controls and patients with cerebellar diseases. Based on reported Dice coefficients, the proposed method outperforms two state-of-the-art methods. The proposed method was then applied to 77 subjects to study the region-specific cerebellar structural differences in three spinocerebellar ataxia (SCA) genetic subtypes. Quantitative analysis of the lobule volumes shows distinct patterns of volume changes associated with different SCA subtypes consistent with known patterns of atrophy in these genetic subtypes.

Kink Formation Dynamics in a Single α-helical Protein

Protein folding remains an open problem despite the progress in understanding the process rate and the success in folding prediction for some small proteins. The reason is the absence of a constructive theoretical framework, both general and specific enough.In earlier papers, we have argued that protein-folding dynamics can be described in terms of solitons of a generalized discrete non-linear Schrodinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles [1]. The soliton manifestation is the pattern helix--loop--helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins and the kink assignment to it [2]. We propose a new mechanism for this process based on the energy transmission along the chain---a disturbance in the latter leads to energy accumulation sufficient to form a kink. We present first insights into the process dynamics by all-atom molecular-dynamics analysis of unfolding of a single alpha-helical protein–--one chain of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK). We suggest an adequate quantification of the side-chain orientation dynamics and also identify some force-field related artefacts.

Oriented Image Foresting Transform Segmentation by Seed Competition

Seed-based methods for region-based image segmentation are known to provide satisfactory results for several applications, being usually easy to extend to multidimensional images. However, while boundary-based methods like live wire can easily incorporate a preferred boundary orientation, regionbased methods are usually conceived for undirected graphs, and do not resolve well between boundaries with opposite orientations. This motivated researchers to investigate extensions for some region-based frameworks, seeking to better solve oriented transitions. In this same spirit, we discuss how to incorporate this orientation information in a region-based approach called “IFT segmentation by seed competition” by exploring digraphs. We give direct proof for the optimality of the proposed extensions in terms of energy functions associated with the cuts. To stress these theoretical results, we also present an experimental evaluation that shows the obtained gains in accuracy for some 2D and 3D data sets of medical images.

Second Order Differences of Cyclic Data and Applications in Variational Denoising

In many image and signal processing applications, as interferometric synthetic aperture radar (SAR), electroencephalogram (EEG) data analysis or color image restoration in HSV or LCh spaces the data has its range on the one-dimensional sphere $\mathbb S^1$. Although the minimization of total variation (TV) regularized functionals is among the most popular methods for edge-preserving image restoration such methods were only very recently applied to cyclic structures. However, as for Euclidean data, TV regularized variational methods suffer from the so called staircasing effect. This effect can be avoided by involving higher order derivatives into the functional. This is the first paper which uses higher order differences of cyclic data in regularization terms of energy functionals for image restoration. We introduce absolute higher order differences for $\mathbb S^1$-valued data in a sound way which is independent of the chosen representation system on the circle. Our absolute cyclic first order difference is just the geodesic distance between points. Similar to the geodesic distances the absolute cyclic second order differences have only values in [0,{\pi}]. We update the cyclic variational TV approach by our new cyclic second order differences. To minimize the corresponding functional we apply a cyclic proximal point method which was recently successfully proposed for Hadamard manifolds. Choosing appropriate cycles this algorithm can be implemented in an efficient way. The main steps require the evaluation of proximal mappings of our cyclic differences for which we provide analytical expressions. Under certain conditions we prove the convergence of our algorithm. Various numerical examples with artificial as well as real-world data demonstrate the advantageous performance of our algorithm.