Extra Degree Of Freedom Research Articles

Anisotropic complexity-free models in modified f(R,T) theory

This paper aims to extend the definition of complexity for a self-gravitating system in f(R,T) theory. We take a static sphere and calculate the corresponding modified field equations as well as the mass function in terms of an effective energy density. The Schwarzschild exterior metric is then taken to determine the junction conditions at the hypersurface. We break the Riemann curvature tensor orthogonally and obtain four scalar functions. We observe that only YTF involves the key factors which determine the structural complexity, thus we call it the complexity factor. Moreover, the field equations contain extra degrees of freedom, thus we require some constraints to close the system. We take the complexity-free condition along with four constraints leading to different models. A particular model is chosen to analyze physical attributes of the resulting solutions for multiple values of the model parameter. It is concluded that the solutions corresponding to Pr=0, a polytropic as well as a linear equation of state show stable behavior for particular values of the model parameter.

Model-independent reconstruction of the interacting dark energy kernel: Binned and Gaussian process

Abstract The cosmological dark sector remains an enigma, offering numerous possibilities for exploration. One particularly intriguing option is the (non-minimal) interaction scenario between dark matter and dark energy. In this paper, to investigate this scenario, we have implemented Binned and Gaussian model-independent reconstructions for the interaction kernel alongside the equation of state; while using data from BAOs, Pantheon+ and Cosmic Chronometers. In addition to the reconstruction process, we conducted a model selection to analyze how our methodology performed against the standard ΛCDM model. The results revealed a slight indication, of at least 1σ confidence level, for some oscillatory dynamics in the interaction kernel and, as a by-product, also in the DE and DM. A consequence of this outcome is the possibility of a sign change in the direction of the energy transfer between DE and DM and a possible transition from a negative DE energy density in early-times to a positive one at late-times. While our reconstructions provided a better fit to the data compared to the standard model, the Bayesian Evidence showed an intrinsic penalization due to the extra degrees of freedom. Nevertheless these reconstructions could be used as a basis for other physical models with lower complexity but similar behavior.

Renyi entropy analysis of a deep convolutional representation for texture recognition

Despite the recent success of convolutional neural networks in computer vision in general, texture images still pose an important challenge to those models, especially when dealing with textures “in the wild”. In this context, deep learning models can benefit from the introduction of features long known to be useful for texture modeling. And that is the case of entropy, a measure of texture regularity that has played an important role in classical computer vision. Based on this observation, here we propose an alternative analysis over deep convolutional neural features based on entropy for texture representation and, particularly, texture classification. More precisely, we couple a module to the convolutional backbone that locally computes the Renyi entropy of the latent representation at multiple levels. The rationale for using Renyi entropy is essentially two-fold: (1) It connects the concept of entropy with multifractal theory, another well explored measure especially in domains of application where we seek some physical interpretation of the descriptors, e.g., in medicine, biology, and others; (2) It has an extra degree of freedom (α parameter) that can be fine-tuned. The main contribution of this study is the development of a strategy that can improve the performance of convolutional neural networks in texture recognition tasks, adding low computational cost. The effectiveness of our method is verified in texture classification of benchmark datasets, as well as in a practical task of plant species identification. Our method achieves a competitive accuracy of 84.5% in the classification of KTH-TIPS-2b and 80.9% in FMD, which are two challenging benchmark databases. Besides, an accuracy of 91.6% is obtained in the plant identification application, to our knowledge outperforming all the results previously published on this task. In both scenarios, the proposed descriptors outperform several approaches from the state-of-the-art, confirming the method potential as a rich and robust solution for texture analysis in general. The results also suggest that information-theoretical measures like entropy can be a reliable source of information to compose a precise and robust latent representation of texture images.

Dielectric resonances of the cylindrical micro/nano cavity within epsilon-near-zero materials.

The dielectric resonances of spherically symmetric micro/nano cavity in zero-index materials have been systematically studied. However, the resonance properties of other shaped dielectric cavities in zero-index materials remain unclear. Here, we theoretically investigate the electromagnetic resonances of the dielectric cavity with cylindrical symmetry in the epsilon-near-zero materials. This kind of cavity supports a set of resonances with strong light confinement, including dipole, quadrupole and higher-order modes with multiple nodes. Furthermore, there is a redshift of the resonance wavelength with an increment of its size, obeying a law as the function of diameter and height. Also, we find that the redshift will be slower for higher-order modes. Through the infinite refractive index contrast and extra degree of freedom, they should have potential application in the enhancement of light-matter interaction and multiple-functional light manipulation in the integrated optical systems.

Higher-order phase field fracture simulation in nearly incompressible viscoelasticity

The phase field modeling of viscoelastic fracture can effectively predict complex crack behavior and offer valuable insights for analyzing time-dependent failure mechanisms. However, its application in nearly incompressible viscoelastic materials presents several numerical challenges, including the volumetric locking and inhibition of crack opening. In addition, the low computational efficiency remains a significant challenge in the development of the phase field models (PFMs). Previous studies have shown that the fourth-order phase field theory can improve the convergence rate of the numerical solution with a smoother phase field. In this study, a fourth-order PFM is proposed, which incorporates the B-bar method and the material penalization to predict the fracture behavior of viscoelastic materials limited by the near compressibility. The additional C1 continuity requirement on the phase field is ensured in the isogeometric framework. No extra degrees of freedom are introduced to resolve the locking problem, which is practical for the PFM, especially in three-dimensional (3D) applications. The loosening of the near incompressibility constraints in the fully damaged zone is achieved by the material penalization, which allows the crack to open freely while preserving the constraints in other regions. The accuracy of the fourth-order PFM is verified through one-dimensional (1D) simulations. Benchmark examples are performed to investigate the numerical behavior of the model. Comparisons between the predicted results and the existing data demonstrate the effectiveness and accuracy of the proposed PFM.

Reducing High Temperature System Development Cycle Time and Cost with Additively Manufactured Connectors

Connectors are a fundamental part of Ozark IC’s high temperature modules from characterization and test packages to Ozark IC’s XNode® data acquisition and single-board computing modules. Development of rugged high temperature electronic systems requires the co-development of similarly rugged high temperature connectors. The design and development of connector solutions enable test and evaluation of high temperature systems which would otherwise require fulfillment of a commercial connector order. There is a nascent supply chain of rugged, high temperature-rated connector designs but manufacturer lead times for such commercial products can exceed an entire design, prototype, and test cycle. Such delays are incompatible with rapid design iterations and fail-fast strategies employed in the development of extreme environment electronics – especially when the design and test cycles can change the requirements or specifications of the connectors. Polymer and ceramic additive manufacturing techniques enable in-house connector fabrication and support a connector co-development cycle that complements the pace and interdependent requirements of high temperature system development. These solutions are simple and reliable under laboratory conditions, operating for thousands of hours at 200 °C [1] and hundreds of hours at 800 °C [2]. The use of proprietary connectors manufactured with additive techniques and digital tooling lends an extra degree of freedom to system design and enables the trade-off of connector with system design specifications that greatly accelerates system ruggedization. Electrical connectors represent the final interface between an electronics module and the outside world. A failure of a connector is a failure of packaging that makes the module opaque to the tester and renders the power and robustness of any electronic system moot.

Observer design based on D-stability and Finsler’s lemma for interconnected Takagi–Sugeno systems with immeasurable premise variables

ABSTRACT This paper deals with the observer design for a class of Interconnected Takagi–Sugeno (TS) systems with Immeasurable Premise Variables (IPV). We first investigate the D-stability of Luenberger-like interconnected multiple observers. However, the resulting constraints can be somewhat conservative due to the use of a common Lyapunov matrix. Then, the so-called Finsler’s lemma is used to relax the D-stability conditions through the introduction of additional slack variables providing more flexibility and extra degrees of freedom. The designed conditions are expressed as Linear Matrix Inequalities (LMIs). The proposed approaches are applied in simulation to a Proton Exchange Membrane Fuel Cell (PEMFC) system and a four-tank system.

Cylindrical Vector Beam Sorting With an Asymmetrical Pancharatnam-Berry Lens

As a type of orthogonal mode with intrinsic turbulence-resilient nature, the cylindrical vector beam (CVB) can offer an extra degree of freedom to increase the information capacity of the optical communications. The sorting of the CVBs is of vital importance for applications in space-division multiplexing communication. Here, we demonstrate numerically and experimentally a CVB sorting with only an asymmetrical Pancharatnam-Berry (PB) lens. The asymmetrical PB lens is composed of two semicircular PB lenses, and it is capable of sorting 11 CVB modes at a wavelength of 1550 nm. The incident CVB can be focused through the asymmetrical PB lens with a focal shift that proportional to the order of the CVB. The proposed sorting device is simple, elegant and efficient, and it may benefit the future applications in mode multiplexing communications.

Electro-momentum coupling tailored in piezoelectric metamaterials with resonant shunts

Local microstructural heterogeneities of elastic metamaterials give rise to non-local macroscopic cross coupling between stress–strain and momentum–velocity, known as Willis coupling. Recent advances have revealed that symmetry breaking in piezoelectric metamaterials introduces an additional macroscopic cross coupling effect, termed electro-momentum coupling, linking electrical stimulus and momentum and enabling the emergence of exotic wave phenomena characteristic of Willis materials. The electro-momentum coupling provides an extra degree of freedom for controlling elastic wave propagation in piezoelectric composites through external electrical stimuli. In this study, we present how to tune the electro-momentum coupling arising in 1D periodic piezoelectric metamaterials with broken inversion symmetry through shunting the inherent capacitance of the individual piezoelectric layers with a resistor and an inductor in series forming a resistor–inductor–capacitor circuit. Guided by the effective elastodynamic theory and homogenization method for piezoelectric metamaterials, we derived a closed-form expression of the electro-momentum coupling in shunted piezoelectric metamaterials. Moreover, we demonstrate the ability to tailor the electro-momentum coupling coefficient and control the amplitudes and phases of the forward and backward propagating waves, yielding tunable asymmetric wave responses. The results of our study hold promising implications for applications involving asymmetric wave phenomena and programmable metamaterials.

A novel optimized dynamic fractional-order MPPT controller using hunter pray optimizer for alleviating the tracking oscillation with changing environmental conditions

Introducing new control strategies in the photovoltaic (PV) system to continuously harvest the maximum power with the changes in environmental conditions is a crucial issue. Therefore, this paper proposes an efficient maximum power point tracker (MPPT) using the perspective of fractional calculus to provide an accurate dynamic response to the rapid changes in environmental conditions. The proposed control scheme is an integration between the fractional proportional–integral (FPI) controller and dynamic variable fractional-order perturb and observe (P&O) MPPT. To optimally identify the proposed MPPT controller parameters, a novel hunter-pray optimizer (HPO) is implemented as it is featured by its efficient balance between exploration and exploitation capacity. The proposed MPPT controller is examined with a series of experiments under dynamically changed environmental conditions. Furthermore, a detailed comparison is conducted versus a set of state-of-the-art including; incremental conductance (INC), basic P&O, MPPT-based particle swarm optimizer(PSO), MPPT-based Grey Wolf Optimizer(GWO), and MPPT-based cuckoo search algorithm (CSA). The results prove that the proposed MPPT is capable to track the global maximum generated power with a notable steady-state response and is almost free of oscillations which ensures an optimal adaptive dynamic performance in response to the rapid variation in the environmental conditions. Moreover, the proposed approach affirms its superiority compared to the set of state-of-the-art techniques in providing the highest maximum power levels in the shortest conversion time. The outcomes provide proof of the remarkable impacts of integrating fractional calculus in enhancing the dynamic response of the proposed MPPT because of the extra degree of freedom that enhance the flexibility of the MPPT.

On Applicability of the Relaxation Spectrum of Fractional Maxwell Model to Description of Unimodal Relaxation Spectra of Polymers.

The relaxation time and frequency spectra are vital for constitutive models and for insight into the viscoelastic properties of polymers, since, from the spectra, other material functions used to describe rheological properties of various polymers can be uniquely determined. In recent decades the non-integer order differential equations have attracted interest in the description of time-dependent processes concerning relaxation phenomena. The fractional Maxwell model (FMM) is probably the most known rheological model of non-integer order. However, the FMM spectrum has not yet been studied and used to describe rheological materials. Therefore, the goal of the present paper was to study the applicability of the relaxation spectrum of FMM to the description of the relaxation spectra of polymers. Based on the known integral representation of the Mittag-Leffler two-parameter function, analytical formulas describing relaxation time and frequency spectra of FMM model were derived. Monotonicity of the spectra was analyzed and asymptotic properties were established. Relaxation frequency spectrum grows for large frequencies with a positive power law, while the relaxation time spectrum decays for large times with a negative power of time. Necessary and sufficient conditions for the existence of the local extrema of the relaxation spectra were derived in the form of two trigonometric inequalities. A simple procedure for checking the existence or absence of the spectra extrema was developed. Direct analytical formulas for the local extrema, minima, and maxima are given in terms of model fractional and viscoelastic parameters. The fractional model parameters, non-integer orders of the stress and strain derivatives of FMM uniquely determine the existence of the spectrum extrema. However, the viscoelastic parameters of the FMM, elastic modulus, and relaxation time affect the maxima and minima of the relaxation spectra and the values of their local peaks. The influence of model parameters on their local extrema was examined. Next, the applicability of the continuous-discrete spectrum of FMM to describe Baumgaertel, Schausberger and Winter (BSW) and unimodal Gauss-like relaxation spectra, commonly used to describe rheological properties of various polymers, was examined. Numerical experiments have shown that by respective choice of the FMM parameters, in particular by respective choice of the orders of fractional derivatives of the stress and strain, a good fit for the relaxation modulus experiment data was obtained for polymers characterized both by BSW and Gauss-like relaxation spectra. As a result, a good approximation of the real spectra was reached. Thus, the viscoelastic relaxation spectrum of FMM, due to the availability of the two extra degrees of freedom (non-integer orders of the stress and strain derivatives), provides deep insights into the complex behavior of polymers and can be applied for a wide class of polymers with unimodal relaxation spectra.

Efficiency-boosted semiconductor optical amplifiers via mode-division multiplexing

Semiconductor optical amplifiers (SOAs) are a fundamental building block for many photonic systems. However, their power inefficiency has been setting back operational cost reduction, circuit miniaturization, and the realization of more complex photonic functions such as large-scale switches and optical phased arrays. In this work, we demonstrate significant gain and efficiency enhancement using an extra degree of freedom of light—the mode space. This is done without changing the SOA’s material design, and therefore high versatility and compatibility can be obtained. Light is multiplexed in different guided modes and reinjected into the same gain section twice without introducing resonance, doubling the interaction length in a broadband manner. Up to 87% higher gain and 300% higher wall-plug efficiency are obtained in a double-pass SOA compared to a conventional single-pass SOA, at the same operating current, in the wavelength range of 1560–1580 nm.

Adaptive phantom node method: An efficient and robust approach towards complex engineering cracks

An efficient and robust approach in the framework of the finite element method for numerical analysis of crack problems is presented. In this method, the discontinuity due to the presence of cracks is described by the technique of phantom nodes. The idea of introducing adaptive mesh refinement along with crack extension into the original phantom node method is presented. The hanging nodes which present in the locally refined mesh is treated by the simple technique of constrained approximation. No additional enrichment functions (and the corresponding extra degrees of freedom) or special elements are involved. As a result, the proposed adaptive phantom node method is almost as simple (and its implementation is as convenient) as the standard finite element method. Numerical results show that the proposed method is able to pass discontinuous patch test accurately and to model crack extension efficiently. In particular, according to its comparison with the original phantom node method in the computation of stress intensity factors, the proposed method consumes less than one percent of the CPU time of the original phantom node method, but it still shows much better accuracy. The capability of the proposed method in modeling multiple cracks, even in complex engineering structures, is also demonstrated.

A new optimal control methodology for improving MPPT based on FOINC integrated with FPI controller using AHA

Conventional maximum power point tracking (MPPT) techniques have remarkable oscillation and drawbacks in tracking the maximum power point (MPP) under rapid climate changes. Therefore, this paper proposes a robust MPPT controller based on the fractional-order incremental conductance method (FOINC) and fractional-order proportional integral controller (FPI) to catch the MPP of the PV system with a high steady state under different levels of radiation. Integrating fractional-order properties with the MPP controller adds an extra degree of freedom for the system, ensuring fast dynamics and high tracking accuracy. An artificial hummingbird algorithm (AHA) is employed to adaptively tune the FPI’s parameters for reliable and self-adapting control. To justify the efficiency of the proposed approach, it is examined with five series of experiments and compared with a set of integer and fractional-based proportional–integral–derivative controllers; moreover, it is validated versus a bunch of state-of-the-art algorithms, including coot bird natural life model (Coot) and chimp optimizer. The comparison reveals that the proposed FOINC integrated with FPI based on AHA can track MPP in 0.1 sec with less oscillation compared with the other approaches that consume more than 0.5 sec; moreover, it provides high levels of harvest power.

Thermal evolution and stability analysis of phenomenologically emergent dark energy model

The phenomenologically emergent dark energy (PEDE) model is a varying dark energy model with no extra degrees of freedom proposed by Li and Shafieloo (Astrophys J 883(1):L3, 2019) to alleviate the Hubble tension. The statistical consistency of the model has been discussed by many authors. Since the model depicts a phantom dark energy that increases with redshift, its cosmic evolution, particularly during the late phase, must be examined. We discover that the model’s Hubble and deceleration parameters display unusual behaviour in the future, which differs from varLambda CDM cosmology. We find the model also follows a distinct evolution in the statefinder plane. The phantom nature of the model leads to the violation of the null energy condition and a decrease in horizon entropy. The asymptotic future epoch also seems to be unstable based on our dynamical system analysis as well as the stability analysis based on dark energy sound speed.

Evolution of the wave function's shape in a time-dependent harmonic potential

Abstract An effective operational approach to quantum mechanics is to focus on the evolution of wave packets, for which the wave function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave function. We review how to extract the effective dynamics for Gaussian wave packets evolving according to the Schrödinger equation with time-dependent potential in a 1 + 1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave function in a time-dependent harmonic potential.

Off‐Resonance Spin‐Locked Metasurfaces Empowered by Quasi‐Bound States in the Continuum for Optical Analog Computing

AbstractMetasurfaces with engineered phase discontinuity offer extra degrees of freedom to control the angular spectrum characteristics of light and can be used to construct planar metalenses with a variety of anomalous functionalities. Here, off‐resonance spin‐locked metasurfaces empowered by quasi‐bound states in the continuum are reported, in order to achieve a concept of hybridized analog computing over both frequency and angular spectrum domains. By introducing two types of asymmetric degrees, high‐quality resonance empowered by the symmetry‐protected bound states in the continuum emerges in an image‐coupled resonance system. Such high‐quality resonance can be excited in a broadband spin‐locked scattering spectrum, promising required functions for scalar multiplication and convolution operations. Off‐resonance meta‐splitter and meta‐deflector are experimentally implemented to verify the concept of hybridized analog computing in two domains, as well as providing an advantage of high robustness against scattering interference from environment. Optical spatial‐frequency processing by engineering the off‐resonance metasurfaces is also discussed. The findings provide an alternative approach toward optical analog computing over multi‐domains.

XFVM modelling of fracture aperture induced by shear and tensile opening.

In reservoir simulation, it is important to understand the mechanical behaviour of fractured rocks and the effect of shear and tensile displacements of fractures on their aperture. Tensile opening directly enhances the fracture aperture, whereas shear of a preexisting rough-walled fracture creates aperture changes dependent on the local stress state. Since fracture dilatation increases reservoir permeability, both processes must be included in a realistic and consistent manner into the mechanical reservoir simulation model. Here, we use the extended finite volume method (XFVM) to conduct flow and geomechanics simulations. In XFVM, fractures are embedded in a poroelastic matrix and are modelled with discontinuous basis functions. On each fracture segment the tractions and compressive forces are calculated, and one extra degree of freedom is added for both the shear and tensile displacement. In this particular XFVM implementation we assume that linear elasticity and steady state fluid pressure adequately constrain the effective stress. In this paper, shear dilation is not calculated a posteriori, but it enters the equations such that aperture changes directly affect the stress state. This is accomplished by adding shear dilation to the displacement gradients and therefore ascertains a consistent representation in the stress-strain relations and force balances. We illustrate and discuss the influence of this extra term in two simple test cases and in a realistic layer-restricted two-dimensional fracture network subjected to plausible in situ stress and pore pressure conditions.

Modified gauge-unfixing formalism and gauge symmetries in the noncommutative chiral bosons theory

Abstract We use the gauge-unfixing (GU) formalism framework in a two-dimensional noncommutative chiral bosons (NCCB) model to disclose new hidden symmetries. That amounts to converting a second-class system to a first-class one without adding any extra degrees of freedom in phase space. The NCCB model has two second-class constraints —one of them turns out as a gauge symmetry generator while the other one, considered as a gauge-fixing condition, is disregarded in the converted gauge-invariant system. We show that it is possible to apply a conversion technique based on the GU formalism direct to the second-class variables present in the NCCB model, constructing deformed gauge-invariant GU variables, a procedure which we name here as modified GU formalism. For the canonical analysis in noncommutative phase space, we compute the deformed Dirac brackets between all original phase space variables. We obtain two different gauge-invariant versions for the NCCB system and, in each case, a GU Hamiltonian is derived satisfying a corresponding first-class algebra. Finally, the phase space partition function is presented for each case allowing for a consistent functional quantization for the obtained gauge-invariant NCCB.

Offshore wind energy prospects for power-to-direct air capture and power-to-gas

Direct air capture of carbon dioxide (CO2) is technically a feasible solution for reducing atmospheric CO2 concentrations at scale, building on decades of global research. However, powering such systems even partially with CO2-intensive fossil fuels results in more CO2 emissions. This paper presents a novel energy management strategy (EMS) to further explore modular offshore wind energy off Canada's West Coast via power-to-direct air capture and power-to-gas systems. The system architecture includes a 15 MW wind turbine paired with a hydrogen energy storage system, i.e. hydrogen production and storage, and direct air capture (DAC) units. Hydrogen production from wind generation is stored and used to offer two key benefits: to deliver the thermal loads of the DAC system, and to meet hydrogen demand for external consumers. The proposed EMS offers an extra degree of freedom to operate the designed system by setting the priority either to maximize the amount of CO2 capture or to maximize the amount of H2 production for external consumers. In particular, the study incorporates dynamic mathematical modeling and constraints formulation for the aforementioned scenarios; DAC priority for CO2 capture and H2 for external hydrogen demand satisfaction. The effectiveness of the proposed EMS is shown through extensive simulations with different seasonal conditions.