Formula For Energy Research Articles

Action-rule-based cognitive control enables efficient execution of stimulus-response conflict tasks: a model validation of Simon task performance.

The human brain can flexibly modify behavioral rules to optimize task performance (speed and accuracy) by minimizing cognitive load. To show this flexibility, we propose an action-rule-based cognitive control (ARC) model. The ARC model was based on a stochastic framework consistent with an active inference of the free energy principle, combined with schematic brain network systems regulated by the dorsal anterior cingulate cortex (dACC), to develop several hypotheses for demonstrating the validity of the ARC model. A step-motion Simon task was developed involving congruence or incongruence between important symbolic information (illustration of a foot labeled "L" or "R," where "L" requests left and "R" requests right foot movement) and irrelevant spatial information (whether the illustration is actually of a left or right foot). We made predictions for behavioral and brain responses to testify to the theoretical predictions. Task responses combined with event-related deep-brain activity (ER-DBA) measures demonstrated a key contribution of the dACC in this process and provided evidence for the main prediction that the dACC could reduce the Shannon surprise term in the free energy formula by internally reversing the irrelevant rapid anticipatory postural adaptation. We also found sequential effects with modulated dip depths of ER-DBA waveforms that support the prediction that repeated stimuli with the same congruency can promote remodeling of the internal model through the information gain term while counterbalancing the surprise term. Overall, our results were consistent with experimental predictions, which may support the validity of the ARC model. The sequential effect accompanied by dip modulation of ER-DBA waveforms suggests that cognitive cost is saved while maintaining cognitive performance in accordance with the framework of the ARC based on 1-bit congruency-dependent selective control.

An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension

An energy formula for fully nonlinear degenerate parabolic equations in one spatial dimension

H dissolution and desorption near He-V complexes in W surfaces with different orientations

Understanding the influence of helium-vacancy (He-V) complexes on hydrogen (H) behaviors in different tungsten (W) surfaces is critical for designing new plasma-facing materials to inhibit H retention and surface damage under H-He-neutron synergetic irradiation. DFT calculations are performed to explore H dissolution and desorption near He-V complexes in W (110), W (100) and W (111) surfaces. We found that, it is most difficult for H dissolution but easiest for H trapping by He-V complexes in the W (110) surface, while the opposite is true in the W (111) surface. When He-V complexes are near W surfaces, the difficulty levels of H diffusion from bulk to surface and desorption increased in the order of (100), (110), and (111). Therefore, the W (110) surface that can inhibit H dissolution would be the best while the W (111) the worst for resisting H retention and surface damage. Based on these mechanisms, we have further proposed a general formula of potential energy to describe H dissolution, diffusion and trapping from surface into bulk in metals.

Design and Optimization of Complex High-Frequency Electromagnetic Treatment Cavity

High-frequency electromagnetic water treatment devices play a crucial role in the scale inhibition and fouling control process of industrial water treatment. They are widely used in various factories and can be classified into coaxial treatment cavities and coil-wound treatment cavities. To address the issues of low energy distribution at the edge of the coaxial treatment cavity and weak peak energy in the coil-wound treatment cavity, which result in unstable scale inhibition and fouling control effectiveness, this study derives a numerical calculation formula for electromagnetic energy in a complex treatment cavity based on the theories of active polarization and quasi-static field. A complex high-frequency electromagnetic water treatment device is designed using this formula, and the internal structure of the treatment cavity is visually analyzed using simulation software. Through the optimization of the complex treatment cavity’s structure, the optimal range of the anode-cathode radius ratio is determined. The research results show that the energy distribution in the complex treatment cavity is significantly higher than that in the coaxial and coil-wound cavities. This study provides theoretical and practical guidelines for the design of high-frequency electromagnetic water treatment device cavities.

Multicomponent solutions: Combining rules for multisolute osmotic virial coefficients.

This paper presents an exploration of a specific type of a generalized multicomponent solution model, which appears to be first given by Saulov in the current explicit form. The assumptions of the underlying theory and a brief derivation of the main equation have been provided preliminarily for completeness and notational consistency. The resulting formulae for the Gibbs free energy of mixing and the chemical potentials are multivariate polynomials with physically meaningful coefficients and the mole fractions of the components as variables. With one additional assumption about the relative magnitudes of the solvent-solute and solute-solute interaction exchange energies, combining rules were obtained that express the mixed coefficients of the polynomial in terms of its pure coefficients. This was done by exploiting the mathematical structure of the asymmetric form of the solvent chemical potential equation. The combining rules allow one to calculate the thermodynamic properties of the solvent with multiple solutes from binary mixture data only (i.e., each solute with the solvent), and hence, are of practical importance. Furthermore, a connection was established between the osmotic virial coefficients derived in this work and the original osmotic virial coefficients of Hill found by employing a different procedure, illustrating the equivalency of what appears to be two different theories. A validation of the combining rules derived here has been provided in a separate paper where they were successfully used to predict the freezing points of ternary salt solutions of water.

Kittel’s molecular zipper model on Cayley trees

Kittel’s 1D model represents a natural DNA with two strands as a (molecular) zipper, which may be separated as the temperature is varied. We define multidimensional version of this model on a Cayley tree and study the set of Gibbs measures. We reduce description of Gibbs measures to solving of a nonlinear functional equation, with unknown functions (called boundary laws) defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give a general formula of free energy depending on the boundary law. Moreover, we find some concrete boundary laws and corresponding Gibbs measures. Explicit critical temperature for occurrence of a phase transition (non-uniqueness of Gibbs measures) is obtained.

A simple formula of the magnetic potential and of the stray field energy induced by a given magnetization

The primary aim of this paper is the derivation and a proof of a simple and tractable formula for the stray field energy in micromagnetic problems. The formula is based on an expansion in terms of a special family of recently discovered functions. It remains valid even if the magnetization is not of constant magnitude or if the sample is not geometrically bounded. The paper continues with a direct and important application which consists in a fast summation technique of the stray field energy. The convergence of this method is established, and its efficiency is proved by various numerical experiments.

Induction Motor Stator Winding Inter-Tern Short Circuit Fault Detection Based on Start-Up Current Envelope Energy.

Inter-turn short circuit (ITSC) is a common fault in induction motors. However, it is challenging to detect the early stage of ITSC fault. To address this issue, this paper proposes an ITSC fault detection method for three-phase induction motors based on start-up current envelope energy. This approach uses Akima interpolation to calculate the envelope of the measured start-up current of the induction motor. A Gaussian window weighting is applied to eliminate endpoint effects caused by the initial phase angle, and the enveloping energy is obtained using the energy formula as the fault feature. Finally, by combining this with the support vector machine (SVM) classification learner, fault detection of ITSC in induction motors is achieved. The experimental results show that the average accuracy of this method reaches 96.9%, which can quickly and accurately detect ITSC faults in asynchronous motors and determine the severity of the faults. Furthermore, the average accuracy of SVM in detecting early ITSC faults under no-load conditions is 98.8%, which is higher than other classification learners, including LR, KNN, and NN. This study provides a new idea for induction motor fault detection and can contribute to induction motor maintenance.

Derivation and reinterpretation of the Fermi-Amaldi functional.

The Fermi-Amaldi correction to the electrostatic self-repulsion of the particle density is usually regarded as a semi-classical exchange functional that happens to be exact only for one- and closed-shell two-electron systems. We show that this functional can be derived quantum-mechanically and is exact for any number of fermions or bosons of arbitrary spin as long as the particles occupy the same spatial orbital. The Fermi-Amaldi functional is also size-consistent for such systems, provided that the factor N in its expression is understood as an orbital occupation number rather than the total number of particles. These properties of the Fermi-Amaldi functional are ultimately related to the fact that it is a special case of the self-exchange energy formula. Implications of our findings are discussed.

Feynman–Kac Formula and Asymptotic Behavior of the Minimal Energy for the Relativistic Nelson Model in Two Spatial Dimensions

We consider the renormalized relativistic Nelson model in two spatial dimensions for a finite number of spinless, relativistic quantum mechanical matter particles in interaction with a massive scalar quantized radiation field. We find a Feynman–Kac formula for the corresponding semigroup and discuss some implications such as ergodicity and weighted Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} to Lq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document} bounds, for external potentials that are Kato decomposable in the suitable relativistic sense. Furthermore, our analysis entails upper and lower bounds on the minimal energy for all values of the involved physical parameters when the Pauli principle for the matter particles is ignored. In the translation invariant case (no external potential), these bounds permit to compute the leading asymptotics of the minimal energy in the three regimes where the number of matter particles goes to infinity, the coupling constant for the matter–radiation interaction goes to infinity and the boson mass goes to zero.

Simulation Analysis and Optimization Design of Electromagnetic Fields in Coaxial Processing Cavities Based on the Theory of Electrostatic Fields

The coaxial processing cavity is an important component of high-frequency electromagnetic water treatment devices. Due to its easy installation, wide applicability, and excellent scale removal effect, it has been widely used in various factories. To study the influence of excitation source waveform, processing cavity length, and anode-cathode radius ratio on the intensity and distribution of the electromagnetic field in the coaxial processing cavity under time-varying fields, this paper derives the numerical calculation formula for electromagnetic energy in the coaxial processing cavity based on the theory of electrostatic fields. The finite element method is used to visualize the intensity and distribution of the electromagnetic field in the coaxial processing cavity. By optimizing the structure of the coaxial processing cavity, the optimal range of the anode-cathode radius ratio is determined. The research results show that, under the conditions of electrostatic field theory, square waves have the maximum electromagnetic energy, the length of the processing cavity does not affect the distribution of the electromagnetic field, and the optimal anode-cathode radius ratio range is 0.375-0.5.

Evolution from gas outburst to coal outburst: An analysis from the perspective of asynchronous transfer difference of gas mass and coal deformation

Considering that coal and gas outburst is a highly complex nonlinear process, the synchronous energy criterion based on the gas expansion energy and the coal deformation potential energy is often adopted to evaluate the hazard. However, the synchronous energy criterion without considering the transfer difference of gas mass and coal deformation has defects in describing the evolution characteristics of coal-rock gas dynamic disasters. Hence, it is necessary to investigate the asynchronous characteristics of the gas expansion energy and the coal deformation potential energy. In this study, the deformation characteristics of coal injected with He and CH4 were measured respectively with the aid of a self-developed device for observing the asynchronous characteristics of effective stress and adsorption-induced deformation. Besides, the differentiated propagation characteristics of gas pressure and adsorption-induced deformation were obtained, and the asynchronous propagation starting point and propagation rate difference between them were analyzed and determined. Furthermore, based on the calculation formula of gas expansion energy and coal deformation potential energy, the values and propagation differences of the two types of energy at different times were revealed. Finally, the typical outburst phenomena were explained using the energy asynchronous theory. The following research findings were yielded. The adsorption-induced expansion process lasts longer than the gas pressure reduction process, which is the reason for asynchronous propagation of gas expansion energy and coal deformation potential energy. The coal deformation potential energy can be further divided into mechanical compression strain energy and desorption shrinkage strain energy. In the initial stage of outburst, the main sources of energy are free gas expansion energy and mechanical compression strain energy. As time progresses, the effect of desorption gas expansion energy and desorption shrinkage strain energy gradually strengthens. From the perspective of energy asynchrony, outburst occurrence at a low gas concentration in deep regions and delayed outburst in cross-cut coal uncovering can be explained as the result of dynamic load instability in surrounding stopes brought about by lagging superimposed deformation disturbances after gas desorption, or the result of self-induced lagging shrinkage deformation formed under special boundary conditions. The findings of this study are helpful to guide the design and connection of the prevention and control methods of deep coal-rock gas dynamic disasters.

Deformation of nucleated cells driven by ultrasonic standing waves

The deformation of nucleated cells driven by ultrasonic standing waves in fluid environment is investigated by theoretical analysis and numerical simulation. The nucleated cells are considered to consist of cell membrane, cytoplasm and nucleus The cell membrane is assumed to have in-plane deformation and bending resistances, in which the in-plane deformation is modeled by the generalized Hooke's law, and the bending resistance is modeled by the Helfrich bending energy formula. Due to the acoustic mismatch between the media inside and outside the cell, the generated acoustic radiation stress on the cell membrane causes the nucleated cell to deform. Considering the acoustic scattering of the nucleus, the acoustic radiation stress is formulated by applying the acoustic radiation stress tensor theory. Based on the proposed theoretical model, a finite element model is established to solve the coupling problem of ultrasonic propagation and cell deformation. The analytical solution for the acoustic induced deformation of nucleated cells in the limits of long wavelength and small deformation is given and successfully verifies the finite element model. The results show that the deformation of nucleated cells is much larger than that of enucleated cells due to the effect of the nucleus on wave propagation. The deformation of nucleated cells is significantly affected by nuclear size and nuclear density. This study is helpful to accurately extract the mechanical properties of nucleated cells and further promote the detection of cell-related diseases by acoustic deformation technology.

Improved energy formula for highly excited vibrational states of Kratzer-Fues oscillator

A mixed supersymmetric-algebraic approach is employed to derive an improved Kratzer-Fues energy formula, which describes the highly excited states of vibrating diatomic systems up to the dissociation limit. The approach proposed has been used to reproduce the coherent anti-Stokes Raman spectra generated by the vibrational transitions of the nitrogen molecule 14\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14}$$\\end{document}N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} in the ground electronic state X1Σg+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X^1\\Sigma _g^+$$\\end{document} and the energy levels of dioxygen 16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{16}$$\\end{document}O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} in the ground electronic state X3Σg-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X^3\\Sigma _g^-$$\\end{document}. The model includes v-dependence of the potential depth D0→Dv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_0\\rightarrow D_v$$\\end{document} as well as interatomic equilibrium separation r0→rv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_0\\rightarrow r_v$$\\end{document} and can be used to describe vibrations of diatomic molecules in which nonadiabatic vibrational effects play a significant role. Exact analytical formulae relating the vibrational spectroscopic constants ωe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _e$$\\end{document}, ωexe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _ex_e$$\\end{document} and ωeye\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _ey_e$$\\end{document} to the parameters defining the model proposed are derived. They enable calculation of the spectral parameters or determination of the model parameters from the experimental data using the inverse spectroscopic procedure. It has been proven that the improved Kratzer-Fues oscillator has a finite number of vibrational quantum states, which distinguishes it from the original model, endowed with infinite number of states.

Characteristics of energy evolution and acoustic emission response of concrete under the action of acidic drying-saturation processes cycle

The continuous fluctuation in the acidic mine water level of the underground reservoir will affect the artificial dam's strength and stability. The uniaxial compression test of C25 concrete under different drying-saturation processes cycle (DSPC) numbers and pH solutions were performed. The degradation mechanism of mechanical properties of concrete under acidic DSPC was investigated; the calculation formula for the elastic strain energy at peak stress has been corrected and the energy evolution law has been obtained; besides, the evolution characteristics of acoustic emission (AE) parameters were studied using multi-fractal theory and the precursor characteristics of concrete failure were obtained. The results revealed that increasing the DSPC times or decreasing the pH caused an increase in the saturation moisture content of the concrete, the strain and elastic strain energy of the concrete at peak stress increased, a drop in the ultrasonic velocity, the uniaxial compressive strength (UCS), the elastic modulus (EM) and the overall input energy. The accumulated ringing count and accumulated energy of AE dramatically increased before the concrete was close to failure, and numerous low-frequency and high-amplitude signals started to appear. The information mentioned above might be considered a short-impending warning of concrete failure. During the plastic deformation, the large increase of the multi-fractal parameter Δα and the significant drop of Δf might be viewed as early warning for concrete failure. This research will offer some theoretical direction for artificial dam design and long-term stability monitoring in underground reservoirs.

The optimization method with segmenting iteration strategy for a long-wavelength infrared metalens

Over the past several years, there has been a substantial surge in the utilization of metasurfaces in micro-electronics and micro-optical devices. As one of their applications, metalenses have aroused significant research interest. In this paper, a new optimization method based on micro co-fluctuation model is proposed to optimize the initial metalens for better focusing performance by adjusting the structural dimensions of nanopillars. A segmenting iteration strategy is used to legitimately reduce the computation space. Meanwhile, an improved Harris Hawks Optimizer (IHHO) is proposed to obtain the optimal solutions, in which a new formula for escape energy is defined to promote the diversity of solution space. The optimization results indicate that the proposed optimization method effectively enhances the focusing capability of the initial metalens with a numerical aperture (NA) of about 0.7 and an operating wavelength of 10.6 μm. The maximum field intensity of the central hot spot and the absolute efficiency have increased by approximately 59.02% and 71.13%, respectively, and the full width at half maximum (FWHM) remains nearly the same value, which provides the potential for achieving high-contrast imaging.

Dynamic modeling and vibration analysis of planar pipeline with partial constrained layer damping treatment: Theoretical and experimental studies

As an important portion of pipeline systems, the vibration suppression analysis of the plane pipeline is of great significance for life prediction and vibration control. To reduce pipeline vibration by attaching constrained layer damping (CLD), the vibration characteristics of the Z-shaped pipeline (taking a Z-shaped pipeline in the planar pipeline as an example) with partial CLD treatment are investigated, and a modeling method is proposed. Based on the Timoshenko beam theory, the energy formulas of laminated straight pipeline with CLD and curved pipeline are developed. Artificial springs are introduced to establish the coupling between pipeline segments and consider the clamp constraint. Four kinds of polynomials are compared to expand the displacement functions, and the dynamic equitation is derived by employing the Lagrange equation. The rationality of the model is verified by a FE model and by in-plane and out-of-plane experimental test systems of the Z-shaped pipeline before and after CLD treatment. In addition, the results show that a change in the geometrical parameters of the pipeline can cause frequency alternation. The influence law of CLD thickness on the Z-shaped pipeline in-plane and out-of-plane is inconsistent. The modeling method can further provide a basis for nonlinear vibration analysis of pipeline systems.

New Perspective in the Use of Power Index Formula for Level Energies

New Perspective in the Use of Power Index Formula for Level Energies

Effects of oxide layers on zirconium alloy-steam reaction

In a severe accident of a BWR plant, zirconium alloy of fuel cladding reacts with steam becoming a heat source for core melting and becoming a hydrogen source for hydrogen explosion. There are a lot of publications giving empirical formulas for energy and hydrogen production due to the zirconium alloy-steam reaction. Most of the formulas are based on a parabolic law, which means the reaction rate and hydrogen production rate decrease monotonously with the reaction time due to the protective oxide layers developed on the alloy surface. However, when the oxide layers are defective for some reason, their effectiveness against the reaction is weakened and the reaction rate will increase. In order to confirm the stability of the oxide layers, an integral-type experiment on the zirconium alloy-steam reaction was set up, hydrogen production rate due to the reaction was measured as a function of exposure time and surface temperature, and then, the oxide layers on the specimen were examined after the exposure. It was confirmed that (1) the analytical results based on Cathcart's formula well explained the experimental results, and (2) the hydrogen production rate did not decrease simply with the exposure time but the decrease in effective oxide layer density resulted in loss of protectiveness and the reaction rate increased.

Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines

Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines