Energy Function Research Articles

Dynamics of solitary waves, chaotic behaviors, and Jacobi elliptic wave solutions in telecommunication systems

This research explores bifurcation of a nonlinear model concerning with the telecommunication strait. Possible all phase plane diagrams due to various parametric conditions are found. Derivation of analytical tangled wave propagating solutions following all phase orbits of the corresponding phase portraits are established. As a results, the soliton, shock wave, singular soliton, periodic wave and singular periodic solutions are obtained by direct integration from Hamiltonian energy function. The periodic solutions of the model are formulated in the form of generalized Jacobi elliptic functions, which also provide the solitonic solution setting the value of beta is unity. Additionally, chaotic and quasi-periodic behaviors have been found for a range of parameter values after adding the perturbed term. The perturbed system’s quasi-periodic and chaotic behavior have been demonstrated using sensitivity analysis. Finally, picturesque explorations are delivered exposing effects of exist parameters of the gained wave solutions. The majority of the achieved results are derived for the first time. Moreover, the solutions show that the novel schemes are very simple, outright, fruitful and successful and that they can be used in wide range of other nonlinear partial differential equations (NLPDEs), which create different kinds of dynamical features of other wave model.

Analysis of initial stage of liquid-phase sintering by combined multi-phase-field/discrete-element method

A combined multi-phase-field/discrete-element method in two dimensions is applied to the liquid phase sintering process of blended elemental powders. The boundary migration, diffusion of elements, and phase transformation between two dissimilar particles are calculated using a multi-phase-field method for sintering based on Gibbs energy functions. The sintering shrinkage is computed with the discrete-element method taking account of the neck size and sintering force, which are obtained from a multi-phase-field simulation. In this study, a pair or small cluster consisting of two elemental powders in a binary eutectic alloy is used as a model system. First, the formation of a liquid phase around the contact area between two dissimilar particles above the eutectic temperature of the system, and the motions of the particles due to grain boundary sliding along the liquid films are confirmed. Second, an Sn–Bi system is selected as the real eutectic system, and the sintering behavior of powder compacts with various mixing ratios of Sn and Bi particles is demonstrated. Finally, transient liquid-phase sintering of Sn–Bi system is simulated, that is, the generation and extinction of the liquid phase due to interdiffusion between Sn and Bi particles are calculated.

Analysis of a higher order problem within the second gradient theory

In this note, we study analytically a higher order equation in a semi-infinite cylinder. First, we will recall some basic inequalities and we define the adequate energy function that we need to find our estimates. Then, the spatial energy decay is proved to be of exponential type. Finally, we consider the application to some heat conduction problems.

The absorption spectrum of the H2 14O radioactive isotopologue of water vapour

ABSTRACT The predicted rotation-vibration absorption spectrum of the radioactive isotopically substituted water molecule, H2 14O, is presented. Variational nuclear-motion calculations are performed using the DVR3D software package based on the use of a high-precision potential energy function and an accurate dipole moment surface. Line centres, intensity and Einstein coefficients are calculated, and air pressure broadening coefficients are estimated. The calculation was carried out over a wide wavenumber range from 0 to 25000 cm − 1 and total angular momentum up to J = 20. Isotopologue extrapolation rules based on experimental data on the energy levels of the stable isotopologues H2 16O, H 2 16 O H2 17O and H2 18O were also used to improve the predicted line positions. Spectral ranges best suited to the detection of H2 14O are identified.

Hamiltonian energy in a modified Hindmarsh-Rose model.

This paper investigates the Hamiltonian energy of a modified Hindmarsh-Rose (HR) model to observe its effect on short-term memory. A Hamiltonian energy function and its variable function are given in the reduced system with a single node according to Helmholtz's theorem. We consider the role of the coupling strength and the links between neurons in the pattern formation to show that the coupling and cooperative neurons are necessary for generating the fire or a clear short-term memory when all the neurons are in sync. Then, we consider the effect of the degree and external stimulus from other neurons on the emergence and disappearance of short-term memory, which illustrates that generating short-term memory requires much energy, and the coupling strength could further reduce energy consumption. Finally, the dynamical mechanisms of the generation of short-term memory are concluded.

Tungsten-Based Contrast Agent for Photon-Counting Detector CT Angiography in Calcified Coronaries: Comparison to Iodine in a Cardiovascular Phantom.

Calcified plaques induce blooming artifacts in coronary computed tomography angiography (CCTA) potentially leading to inaccurate stenosis evaluation. Tungsten represents a high atomic number, experimental contrast agent with different physical properties than iodine. We explored the potential of a tungsten-based contrast agent for photon-counting detector (PCD) CCTA in heavily calcified coronary vessels. A cardiovascular phantom exhibiting coronaries with calcified plaques was imaged on a first-generation dual-source PCD-CT. The coronaries with 3 different calcified plaques were filled with iodine and tungsten contrast media solutions equating to iodine and tungsten delivery rates (IDR and TDR) of 0.3, 0.5, 0.7, 1.0, 1.5, 2.0, 2.5, and 3.0 g/s, respectively. Electrocardiogram-triggered sequential acquisitions were performed in the spectral mode (QuantumPlus). Virtual monoenergetic images (VMIs) were reconstructed from 40 to 190 keV in 1 keV increments. Blooming artifacts and percentage error stenoses from calcified plaques were quantified, and attenuation characteristics of both contrast media were recorded. Blooming artifacts from calcified plaques were most pronounced at 40 keV (78%) and least pronounced at 190 keV (58%). Similarly, percentage error stenoses were highest at 40 keV (48%) and lowest at 190 keV (2%), respectively. Attenuation of iodine decreased monotonically in VMIs from low to high keV, with the strongest decrease from 40 keV to 100 keV (IDR of 2.5 g/s: 1279 HU at 40 keV, 187 HU at 100 kV, and 35 HU at 190 keV). The attenuation of tungsten, on the other hand, increased monotonically as a function of VMI energy, with the strongest increase between 40 and 100 keV (TDR of 2.5 g/s: 202 HU at 40 keV, 661 HU at 100 kV, and 717 HU at 190 keV). For each keV level, the relationship between attenuation and IDR/TDR could be described by linear regressions (R2 ≥ 0.88, P < 0.001). Specifically, attenuation increased linearly when increasing the delivery rate irrespective of keV level or contrast medium. Iodine exhibited the highest relative increase in attenuation values at lower keV levels when increasing the IDR. Conversely, for tungsten, the greatest relative increase in attenuation values occurred at higher keV levels when increasing the TDR. When high keV imaging is desirable to reduce blooming artifacts from calcified plaques, IDR has to be increased at higher keV levels to maintain diagnostic vessel attenuation (ie, 300 HU), whereas for tungsten, TDR can be kept constant or can be even reduced at high keV energy levels. Tungsten's attenuation characteristics in relation to VMI energy levels are reversed to those of iodine, with tungsten exhibiting high attenuation values at high keV levels and vice versa. Thus, tungsten shows promise for high keV imaging CCTA with PCD-CT as-in distinction to iodine-both high vessel attenuation and low blooming artifacts from calcified plaques can be achieved.

Determining thermal activation parameters for ferroelectric domain nucleation in BaTiO3 from molecular dynamics simulations

Polarization switching in ferroelectric hysteresis of BaTiO3 proceeds by localized nucleation and subsequent growth of domains of reverse polarization. While this process is driven by the applied electric field, thermal activation can play an important role in domain nucleation. As a consequence of the stochastic nature of thermal activation, coercive fields in small systems exhibit a significant scatter. It is demonstrated that the statistics of coercive fields observed in molecular dynamics simulations is consistent with the statistical distribution expected for field-assisted thermally activated nucleation of reverse polarization domains. The excellent quantitative agreement between the simulation data and the theory of thermally activated processes provides strong evidence that polarization switching occurs by nucleation-and-growth rather than loss of the local minimum of the Gibbs free energy function. In a pristine crystal, switching is controlled by the field at which thermal fluctuations can create a critical nucleus in the bulk (homogeneous nucleation). The analysis of crystals with various vacancy-type defects demonstrates that such defects may enable heterogeneous nucleation at reduced fields. In both cases, the statistical analysis gives access to the respective activation energies, their field dependence, and the sizes of the critical nuclei.

Probabilistic Offline Policy Ranking with Approximate Bayesian Computation

In practice, it is essential to compare and rank candidate policies offline before real-world deployment for safety and reliability. Prior work seeks to solve this offline policy ranking (OPR) problem through value-based methods, such as Off-policy evaluation (OPE). However, they fail to analyze special case performance (e.g., worst or best cases), due to the lack of holistic characterization of policies’ performance. It is even more difficult to estimate precise policy values when the reward is not fully accessible under sparse settings. In this paper, we present Probabilistic Offline Policy Ranking (POPR), a framework to address OPR problems by leveraging expert data to characterize the probability of a candidate policy behaving like experts, and approximating its entire performance posterior distribution to help with ranking. POPR does not rely on value estimation, and the derived performance posterior can be used to distinguish candidates in worst-, best-, and average-cases. To estimate the posterior, we propose POPR-EABC, an Energy-based Approximate Bayesian Computation (ABC) method conducting likelihood-free inference. POPR-EABC reduces the heuristic nature of ABC by a smooth energy function, and improves the sampling efficiency by a pseudo-likelihood. We empirically demonstrate that POPR-EABC is adequate for evaluating policies in both discrete and continuous action spaces across various experiment environments, and facilitates probabilistic comparisons of candidate policies before deployment.

Cross sections of cascade production of photoions after photoionization of the silver atom in the 0.07–100 keV incident photon energy range

The formation of multiply charged Agq+ ions resulting from photoionization and subsequent cascade decay of inner-shell vacancy states is studied using the method of construction and analysis of the cascade decay trees. Cross sections for the cascade production of Agq+ ions, yields of Agq+ ions, and mean photoion charge are calculated as functions of incident photon energy in the range of 70 eV to 100 keV. The results of this study are relevant for developing the strategies of radiotherapy using Ag-based radiosensitizers.

Examining the influence of magnetic field on a donor dopant’s photoionization cross-section in a double quantum box

This study systematically explored the binding energy and the photoionization cross-section (PCS) of a hydrogenic shallow donor impurity within a GaAs double quantum box structure incorporated into a Ga(1−x)Alx As matrix under the influence of an external intense magnetic field. The computations are performed using the effective-mass approximation (EMA) and the finite element method (FEM), taking into account a finite potential across all surfaces of the nanosystem. The results emphasize the significant role of the magnetic field, primarily in enhancing the donor binding energy within the double quantum box system. We demonstrate that increasing the magnetic field results in an augmentation of binding energy across various aluminum concentrations. The PCS of a shallow donor impurity undergoes a blue shift when shifted from the barrier center to the box center, attributed to the increased binding energy. When the double quantum box is subjected to a magnetic field effect, the amplitude peaks of PCS show an elevation coupled with a blue shift. By setting magnetic field values at 0 T, 35 T, or 70 T and varying aluminum concentrations, we observe a shift in the PCS towards higher energy levels along with an increase in peak amplitude. We also study the PCS of the donor impurity as a function of photon energy, mainly examining the effects of box width and barrier width modifications in the double quantum box.

Energy and self-adaption in a memristive map neuron

Both capacitor and charge-controlled memristor (CCM) can regulate the inner energy levels during the release and accumulation of charges in these electronic components. Combination of inductive and capacitive components is crucial to build an oscillatory circuit, and incorporation of a nonlinear resistor is helpful to support nonlinear oscillation under continuous energy exchange between magnetic field and electric field. Relation between physical variables in neural circuits can be described by some equivalent nonlinear oscillators by applying scale transformation on the variables and parameters for the neural circuit, and the energy function becomes available from theoretical approach. In this work, a simple neural circuit coupled with a CCM is designed to obtain a memristive neuron model, and then linear transformation is applied to the sampled variables involved with time scale for time step, a new memristive map is obtained to discuss its energy characteristic and self-controllability under energy flow. The result provides guidance to measure the reliability of maps, and the new derived maps with reliable physical evidences can be further used in digital signal processing.

Systematic schemes for buckling analyses of a subsea bio-inspired non-circular FGM polyhedral liner with an arch invert

This study develops theoretical frameworks for the buckling failure of a non-circular thin-walled liner encased in a cracked pipeline with an arch invert. The buckling performance of the pipeline-liner system is improved by combining the polyhedral profiles and the Functionally Graded Materials (FGM). The liner is close-fitting to the inner surface of the pipeline. The energy function is obtained by assembling the thin-walled shell principle and the theory of minimum potential energy. Then, the nonlinear equilibrium equations and the buckling equations are derived to predict the buckling performances of the FGM polyhedral pipeline-liner system with an arch invert. Moreover, the present buckling behaviors of the system are compared with other available results, and good agreements are accomplished when the FGM polyhedral liner degenerates into an FGM circular liner or a homogeneous polyhedral liner. In addition, an enhancement coefficient is defined as the ratio of the buckling pressure of a polyhedral liner to a circular one. Finally, several key geometric and material parameters are examined to quantify their effects on the buckling behavior of the FGM polyhedral pipeline-liner system with an arch invert. These parameters are volume fraction exponents, polyhedral shapes, and thickness-to-radius ratios, respectively.

An elastoplastic phase-field model for quasi-static fracture of nickel-based super-alloys

In the present study, an elastoplastic phase-field model of quasi-static fracture in ductile materials is proposed in the variational framework for J2 plasticity with isotropic hardening, which is suitable to describe the quasi-static behavior of metals as investigated in the performed experiments. These contributions include: (1) the free energy functions for coupling elastic response, plastic yielding and damage evolution are established. (2) The new elastic and plastic energy degradation functions are constructed to quantitatively describe the relationship between energy release and phase-field evolution of elastoplastic materials. (3) Damage evolution and plastic yielding criteria are derived. (4) From a numerical point of view, we derive the governing equations and the corresponding weak forms and the overall solution procedure for the phase-field model is given via the use of a return-mapping algorithm. This phase-field model was validated by a series of tensile experiments on Inconel 718 nickel-based super-alloys standard specimens. In order to compare the simulation results with the experimental results more comprehensively, the digital image correlation (DIC) technique is applied to experimentally investigate the specimen deformation information. In addition, to verify the potential of the model to capture complex cracks, we performed Nooru-Mohamed tests. The numerical simulation results are in good agreements with the results of previous experimental work.

Multiple DC Modulation Coordination Strategies Based on Transient Energy Function and Deep Deterministic Policy Gradient Algorithm

Ultra-low-frequency oscillation (ULFO) is a new problem of frequency stability in asynchronous network back-end power networks. The negative damping provided by hydropower units is the direct cause of ultra-low-frequency oscillation, and DC modulation is an effective means of suppressing system frequency oscillation. Based on the transient energy function and the limitation of DC modulation, this paper analyzes the conditions of suppressing system oscillation by DC modulation from the perspective of energy. The weight of unit energy participation is defined, and the calculation formula of transient oscillation energy in a certain oscillation mode is derived. DC modulation sensitivity is then used to create a DC modulation sequence table based on the Prony identification approach. Ultimately, the DC involved in the modulation is identified using the DC modulation sequence table and the transient oscillation energy, and the Deep Deterministic Policy Gradient (DDPG) algorithm is used to optimize the chosen DC modulation parameters.

Plug-and-play multi-dimensional attention module for accurate Human Activity Recognition

Unlike image data, Human Activity Recognition (HAR) data is collected through sensors placed on different parts of the body. Each sensor may have varying importance for different human actions. Attention mechanisms can dynamically identify the significance of signals from different sensors. However, existing attention modules often operate along channel or spatial dimensions, producing one-dimensional or two-dimensional weights, and considering neurons within every channel or spatial location as equivalent. This might constrain their capacity to acquire more distinctive cues. In this paper, we present a novel Three-Dimensional Weight Attention Module (WAM) that considers both spatial and weight information of each channel. Specifically, we commence by introducing an energy function and subsequently assess the significance of each neuron through optimization. Unlike conventional channel or spatial attention modules, this module can compute 3D attention weights for feature maps without additional parameters. Experiments conducted on four diverse HAR datasets showcase that the Three-Dimensional Weight Attention Module can seamlessly integrate with convolutional models, significantly enhancing model performance without introducing extra computational burden. To further highlight the utility of WAM, we measure the actual inference time on an embedded platform.

Quantification of aluminium and silicon‐containing materials using Ag Lα X‐rays

In recent years, instrument manufacturers have been providing laboratory‐based HAXPES (hard X‐ray photoelectron spectroscopy) instruments that have monochromated silver Lα, chromium Kα and gallium Kα X‐ray sources. To be more than a qualitative tool, two things are required: calibration of the signal intensity as a function of kinetic energy (spectrometer response function) and relative sensitivity factors. This is now possible because of routines being available to generate the spectrometer response functions for dual Al Kα/Ag Lα X‐ray sources and the availability of Cant average matrix relative sensitivity factors (AMRSFs). However, to improve accuracy when using the Cant AMRSF care needs to be taken in the definition of the peak areas being used. This is because they need to include the total intrinsic signal that often extends beyond the main peak. This is a particular challenge when quantifying using the Al 1s peak generated with Ag Lα X‐rays as some of the intrinsic signal overlaps with the Al KLL Auger peak. When materials include both aluminium and silicon atoms, the Si 2s and 2p peaks sit upon extended signals coming from the Al 2s and 2s peaks, respectively. Thus, quantification should be limited to using the main peak area, which necessitates different relative sensitivity factors (RSFs). Using polydimethylsiloxane (PDMS) and sapphire (Al2O3) as model systems, experimental RSFs have been determined for use with the main peaks for O 1s, Al 1s, Al2s Al 2p, Si 1s, Si 2s and Si 2p subshells normalized to the RSF of the carbon 1s main peak.

Anisotropic evolution of viscous strain in soft biological materials

We propose a model for anisotropic viscoelastic biological materials that can handle large deformations, based on the kinematic assumption that the reinforcing fibre structure undergoes affine deformation with the underlying matrix. A generalized orientation tensor approach is used to account for the dispersion of the fibres. Moreover, we consider a strain energy function that features both an elastic and an overstress component, corresponding to distinct natural states. As a consequence of this choice, the remodelled state is not necessarily stress-free, and the material does not completely relax the stress. Notably, we consider that viscous remodelling also alters the fibre distribution, leading to a dependence of the overstress energy on the remodelled orientation tensor. An anisotropic evolution equation for the viscous strain is then derived, which has five distinct characteristic times if a single fibre family is considered and requires no additional assumptions on the viscous spin. To implement the model, we prove that the evolution of the viscous strain can be recast in a variational form by an Onsager variational principle. Finally, we discuss the algorithm used for the simulations and show numerical examples that serve as benchmark test cases for viscoelastic materials.

Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies.

Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.

Spatially-resolved UV-C emission in epitaxial monolayer boron nitride

We report hyperspectral imaging in the UV-C spectral domain in epitaxial monolayers of hexagonal boron nitride (hBN). Under quasi-resonant laser excitation, the UV-C emission of monolayer hBN consists in resonant Raman scattering and photoluminescence, which appear to be spatially uncorrelated. Systematic measurements as a function of the excitation energy bring evidence of a photoluminescence singlet at ∼6.045 eV. The spatial variations of the photoluminescence energy are found to be around ∼10 meV, revealing that the inhomogeneous broadening is lower than the average photoluminescence linewidth of ∼25 meV, a value close to the radiative limit in monolayer hBN. Our methodology provides an accurate framework for assessing the opto-electronic properties of hBN in the prospect of scalable hBN-based devices fabricated by epitaxy.

The intrinsic switching field of single domain ferromagnetic particles

The intrinsic switching field defined as the minimum field to induce spontaneous magnetic reversal is calculated at finite temperatures for a uniaxially anisotropic single domain particle using a formalism based on the generalized free energy function of the system. For a fine ferromagnetic particle coupled to a constant temperature heat bath, the switching field is smaller than the field predicted by the Stoner-Wohlfarth (SW) theory and the difference is dependent on the direction of the applied field resulting in breaking of the symmetry of the SW astroid.