Additional Degrees Of Freedom Research Articles

Hybrid equilibrium formulation with adaptive element side orientation for cohesive crack prediction

AbstractThe present article proposes an hybrid equilibrium element (HEE) formulation for the prediction of cohesive fracture formation and propagation with the crack modelled by extrinsic interface embedded at element sides. The hybrid equilibrium element formulation can model high order (quadratic, cubic and quartic) stress fields which strongly satisfy homogeneous equilibrium equations, inter‐element and boundary equilibrium equations. The HEE can implicitly model both the initially rigid behaviour of an extrinsic interface and its debonding condition with separation displacement and softening. The extrinsic interface is embedded at the element sides and its behaviour is governed by means of the same degrees of freedom of HEE (generalized stresses), without any additional degree of freedom. The proposed extrinsic cohesive model is developed in the thermodynamic framework of damage mechanics. The proposed crack propagation criterion states that crack grows when the maximum principal stress reaches the tensile strength value, in a direction orthogonal to the principal stress direction. The crack is embedded at an element side and the mesh around crack tip is adapted, by rotation of the element sides, in order to have the interface aligned to the crack growth direction. Three classic two‐dimensional problems of fracture propagation are numerically reproduced and the results compared to the experimental data or to the other numerical results.

Finsler–Randers–Sasaki gravity and cosmology

We present for the first time a Friedmann-like construction in the framework of an osculating Finsler–Randers–Sasaki (F–R–S) geometry. In particular, we consider a vector field in the metric on a Lorentz tangent bundle, and thus the curvatures of horizontal and vertical spaces, as well as the extra contributions of torsion and non-linear connection, provide an intrinsic richer geometrical structure, with additional degrees of freedom, that lead to extra terms in the field equations. Applying these modified field equations at a cosmological setup we extract the generalized Friedmann equations for the horizontal and vertical space, showing that we obtain an effective dark energy sector arising from the richer underlying structure of the tangent bundle. Additionally, as it is common in Finsler-like constructions, we obtain an effective interaction between matter and geometry. Finally, we consider a specific model and we show that it can describe the sequence of matter and dark-energy epochs, and that the dark-energy equation of state can lie in the quintessence or phantom regimes, or cross the phantom divide.

Customizable polarization-selective narrowband meta-filters using a printable UV-curing nanocomposite.

Low-cost nanocomposite metasurfaces have demonstrated attractive potential to replace the equivalent dielectric metasurfaces for light engineering. However, the resonance characteristics of embedded structures in nanocomposite metasurfaces have not been further analyzed beyond the effective refractive index. Herein, we have proposed customizable polarization-selective narrowband meta-filters using ultraviolet-curable (UV) nanocomposites. As an additional degree of freedom, near-field effects between highly concentrated doped nanoparticles can enhance the Mie resonance of the low aspect ratio (AR = 0.2) meta-units. The surface lattice resonances (SLRs) of meta-filters can be coupled with enhanced Mie resonances of individual meta-units to realize tunable narrowband (FWHM ∼0.007λ) reflections with intensities near unity. Meanwhile, the polarization-selective properties of the reflection peaks can be tuned by optimizing the asymmetric lattice. Such proposed new-generation customizable meta-filters will offer, to our knowledge, novel strategies for filtering specific near-infrared polarized fluorescence in the integrated imaging systems.

Motion state factor driven for doubly-curved shallow shell deformation reconstruction

The conventional shape sensing method, based on C0 continuity, is recognized for its computational efficiency. However, it is prone to shear locking due to low-order polynomial interpolation in shell analysis, introducing two primary challenges. Firstly, it lacks consideration for C1 continuity. Secondly, existing high-order polynomial interpolation methods significantly increase the number of degrees of freedom (DOF), reducing computational efficiency. Therefore, a brand-new real-time structural health monitoring (SHM) method driven by motion state factor instead of nodal factors is proposed. This method accommodates all deformation modes of shallow shells with C1 continuity and improves the shape function's order without additional DOF. It begins with deriving motion states from compatibility equations, leading to a polynomial shape function expression. Subsequently, conversion equations for real constants and DOF are developed, establishing a least-squares model for theoretical strains and measured values. Following that, the higher-order element formula, optimized for minimal DOF, is then inferred from varied displacement data. Finally, simulations and experiments demonstrate this method's effectiveness, accuracy, and reliability in analyzing shallow shell elements.

Are f(R, Matter) theories really relevant to cosmology?

We examine f(R, Matter) theories that directly couple the curvature R or R μν with the matter sector in the action, in addition to the universal coupling. We argue that if the matter sector includes the Standard Model (SM), such theories are either inconsistent or already excluded by experiments unless they are a rewriting of f(R) gravity or general relativity. If these theories genuinely couple the SM to curvature, they suffer from the presence of ghost states at energies within their domain of application for cosmological purposes. Therefore, we raise questions about their relevance to cosmology. Moreover, if such theories do not include the SM, they should just be seen as scalar-tensor, vector-tensor, …, theories, depending on the additional degrees of freedom. They should thus be studied accordingly.

Design of finite‐time convergent functional observer for descriptor systems: Application to fault estimation

AbstractIn this paper, a finite‐time functional observer design for linear time‐invariant descriptor systems is presented. A generalized observer based on additional degrees of freedom is developed. This observer can be considered of a general structure since the existing proportional observer (PO) and proportional‐integral observer (PIO) constitute its particular cases. The main contribution is to generate a finite‐time convergent functional observer for descriptor systems by combining two generalized functional observers. The obtained results are applied to the simultaneous state, sensor, and actuator faults estimation. A numerical example is given to illustrate the approach. The obtained results show that the observer is robust in presence of uncertainties, compared to its particular cases.

Performance enhancement of a three-phase grid-connected PV inverter system using fractional-order integral sliding mode controls

Grid-integrated photovoltaic (PV) systems hold significant promise for sustainable energy production. However, these systems often struggle with maintaining energy quality and stability in the face of fluctuating conditions. To address these challenges, this study proposes the use of fractional-order integral sliding mode control (FO-ISMC) for grid-connected PV systems. The system comprises solar panel arrays, a DC/DC boost converter with its controller, and a three-phase inverter integrated into the utility grid. The primary goals of this study are to maximize power extraction from the PV system and to regulate system currents, thereby improving effectiveness and power quality. The proposed method is further refined using the particle swarm optimization (PSO) algorithm to fine-tune parameter settings. By optimizing the command gains of the FOI-SMC, the PSO algorithm enhances system performance and stability. Leveraging fractional-order and integral terms provides the control signal with additional degrees of freedom, enhancing system performance in the presence of internal and external disturbances. Simulation results demonstrate the effectiveness of the proposed controller compared to the classical controller, where in the case of Irradiation taking the value of 500 W/m2, the proposed strategy reduced the values of constant voltage, active power, and reactive power by percentages estimated at 88.18%, 90%, and 70%, respectively, compared to the traditional strategy. Also, the overshoot value of active power was reduced in all completed cases compared to the traditional strategy by percentages estimated at 53.57%, 66.66%, and 65%, respectively. The proposed strategy reduced the response time of reactive power in all cases compared to the traditional strategy by percentages estimated at 58.59%, 28.80%, and 75%, respectively. These ratios show the high performance of the proposed control in improving the characteristics of the studied system compared to traditional control based on PI control.

Low-order finite element method for the static and vibration analysis of an antenna pedestal

In this work, an effective algorithm is developed for the static and vibration analysis of antenna pedestal, which can well balance the modelling efficiency and computational accuracy. At first, the antenna pedestal is discretized into a set of low-order tetrahedral elements that can be automatically generated. Then, the face-based smoothing domains are constructed based on the faces of the low-order tetrahedral mesh. With the help of strain smoothing technique, the system stiffness matrices are calculated in these smoothing domains and finally, the static and vibration responses of the antenna pedestal are obtained based on the related system equations. There is no need to add any penalty parameters or additional degrees of freedom. Numerical results demonstrate that the present algorithm can achieve much better accuracy and higher convergence rate than traditional FEM, which can be regarded as an efficient tool for the structural analysis of antenna pedestal.

Multi-axis fields boost SABRE hyperpolarization

The inherently low signal-to-noise ratio of NMR and MRI is now being addressed by hyperpolarization methods. For example, iridium-based catalysts that reversibly bind both parahydrogen and ligands in solution can hyperpolarize protons (SABRE) or heteronuclei (X-SABRE) on a wide variety of ligands, using a complex interplay of spin dynamics and chemical exchange processes, with common signal enhancements between 103 and 104. This does not approach obvious theoretical limits, and further enhancement would be valuable in many applications (such as imaging mM concentration species in vivo). Most SABRE/X-SABRE implementations require far lower fields (μT-mT) than standard magnetic resonance (>1T), and this gives an additional degree of freedom: the ability to fully modulate fields in three dimensions. However, this has been underexplored because the standard simplifying theoretical assumptions in magnetic resonance need to be revisited. Here, we take a different approach, an evolutionary strategy algorithm for numerical optimization, multi-axis computer-aided heteronuclear transfer enhancement for SABRE (MACHETE-SABRE). We find nonintuitive but highly efficient multiaxial pulse sequences which experimentally can produce a sevenfold improvement in polarization over continuous excitation. This approach optimizes polarization differently than traditional methods, thus gaining extra efficiency.

A large deformation gradient theory for glassy polymers by means of micromorphic regularization

AbstractCold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization.

An Efficient Local Artificial Boundary Condition for Infinite Long Finite Element Euler–Bernoulli Beam

To solve the wave propagation problems of the Euler–Bernoulli beam in an unbounded domain effectively and efficiently, a new local artificial boundary condition technology is proposed. It replaces the residual right-hand side of the truncated discrete equation with an equivalent linear algebraic system. First, the equivalent Schrodinger equation is discussed. Its artificial boundary condition is obtained by first rationalizing the Dirichlet-to-Neumann condition in the frequency domain with a Pade approximation and then inverse transforming each Pade term back into the time domain by introducing auxiliary degrees of freedom. Frequency shifting is employed such that it performs better near a prescribed frequency. Then, the artificial boundary condition of the finite element Euler–Bernoulli beam is obtained by simple algebraic manipulations on that of the corresponding Schrodinger equation. This method only makes local changes to the original truncated discrete dynamic system and thus is very efficient and easy to use. The accuracy of the proposed method can be improved by using more Pade terms and a proper shift frequency. The numerical example shows, with only a few additional degrees of freedom, the proposed artificial boundary condition effectively eliminates the spurious reflection. The idea of the proposed method can also be used in other dispersive wave systems.

An extended isogeometric boundary element formulation for three-dimensional linear elastic fracture mechanics

This paper presents a novel extended isogeometric boundary element formulation (XIGABEM) for three-dimensional linear elastic fracture mechanics. The formulation utilises the Dual BEM to accommodate coincident geometries for opposing crack surfaces, and inherits the well-known advantages of the NURBS basis as other isogeometric implementations. The originality herein involves the extension of the above-mentioned scheme to 3D using enrichment functions derived from asymptotic solutions for near-field crack tip displacements, in which Williams’ expansions are used on the crack surfaces and on the boundaries crossed by the crack front. Besides, Heaviside functions enrich external boundaries and allow the displacement discontinuity modelling. As with most enriched formulations, additional degrees of freedom are introduced; novel strategies are presented for the generation of auxiliary equations to recover a square system.Another key element of the proposed scheme is that the stress intensity factors are recovered directly from the solution vector and no post processing is required. Four applications demonstrate the formulation robustness, with results of models having comparatively few degrees of freedom comparing well against classical and other published results.

Adaptive anisotropic Bayesian meshing for inverse problems

We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that errors arising from the discretization can be detrimental for ill-posed inverse problems, as discretization error behaves as correlated noise. While this problem can be avoided with a discretization fine enough to decrease the modeling error level below that of the exogenous noise that is addressed, e.g. by regularization, the computational resources needed to deal with the additional degrees of freedom may increase so much as to require high performance computing environments. Following an earlier idea, we advocate the notion of the discretization as one of the unknowns of the inverse problem, which is updated iteratively together with the solution. In this approach, the discretization, defined in terms of an underlying metric, is refined selectively only where the representation power of the current mesh is insufficient. In this paper we allow the metrics and meshes to be anisotropic, and we show that this leads to significant reduction of memory allocation and computing time.

One-dimensional extended Su–Schrieffer–Heeger models as descendants of a two-dimensional topological model

The topological phase diagrams and finite-size energy spectra of one-dimensional extended Su–Schrieffer–Heeger (SSH) models with long-range hoppings on the trimer lattice are investigated in detail. Due to the long-range hoppings, the band structure of the original SSH model becomes more complicated and new phases with the large Zak phase can emerge. Furthermore, a seeming violation of bulk-edge correspondence occurs in the one-dimensional topological system whose band topology stems from the inversion symmetry. The one-dimensional models are mapped onto a two-dimensional topological model when a parameter of the one-dimensional models is regarded as an additional degree of freedom. As Fourier components of the derived two-dimensional model, phase boudaries and the finite-size spectra of one-dimensional models can be recovered from the model in the higher spatial dimensions. Then the origin of edge modes of one-dimensional models can be understood from two dimensions and we give a reasonable explanation of the violation of bulk-edge correspondence in one spatial dimension. In fact, we may give a general perspective that the topological properties of one-dimensional (lower-dimensional) systems can be found their origin from two-dimensional (higher-dimensional) systems.

Modeling mechanical waves propagation in flexoelectric solids

In this paper, the propagation of mechanical waves in flexoelectric solids with the consideration of both the direct and converse flexoelectric effects is studied via a collocation mixed finite element method (MFEM). The dynamic effects associated with mechanical waves propagation are accounted by introducing the kinetic energy in the Hamilton’s principle. In the proposed collocation MFEM, a quadratic polynomial is independently assumed for each component of the mechanical strain and electric field. The independently assumed mechanical strain and electric field are collocated with their counterparts computed from the displacement and electric potential at 9 Gaussian quadrature points. Thus, except for the fundamental field variables, no additional degrees of freedom (DOFs) are introduced. By performing the numerical experiments using the collocation MFEM, it is found that due to the direct flexoelectric effect, the propagation of mechanical waves can result in electric polarization in materials. Besides, the converse flexoelectric effect can induce mechanical waves when there are non-uniform transient electric field applied to the material. Numerical results indicate that by increasing the loading speed of the time varying mechanical displacement load, the direct flexoelectric effect associated with the mechanical strain gradient could be significantly enhanced.

A Study on Fractional Power-Law Applications and Approximations

The frequency response of the fractional-order power-law filter can be approximated by different techniques, which eventually affect the expected performance. Fractional-order control systems introduce many benefits for applications like compensators to achieve robust frequency and additional degrees of freedom in the tuning process. This paper is a comparative study of five of these approximation techniques. The comparison focuses on their magnitude error, phase error, and implementation complexity. The techniques under study are the Carlson, continued fraction expansion (CFE), Padé, Charef, and MATLAB curve-fitting tool approximations. Based on this comparison, the recommended approximation techniques are the curve-fitting MATLAB tool and the continued fraction expansion (CFE). As an application, a low-pass power-law filter is realized on a field-programmable analog array (FPAA) using two techniques, namely the curve-fitting tool and the CFE. The experiment aligns with and validates the numerical results.

The dynamic organicity theory of consciousness: how consciousness arises from the functionality of multiscale complexity in the material brain

The fine structure of consciousness is temporally experienced. This makes possible a dynamic organicity theory of consciousness through disunified order in the pre-, sub- and noncognitive levels of causal processes and dynamics. This multilevel approach is based on functional systems where space is implicitly grounded as changeable boundary conditions (due to organicity), and energy capture and storage under energy flow entail structuring intrinsic information (as both hidden thermodynamic energy and hidden thermodynamic information). The use of anaesthesia indicates consciousness disappears when there is an obliteration of intrinsic information within membrane protein amino acids, suggesting that quantum-thermal fluctuations of the electromagnetic field can be functional and non-vacuous. The origin of thermo-qubit syn-tax is derived from the principle of self-reference as the syntax of consciousness. In addition to the classical Brownian motion of macroscopically observable mean values, the negentropically derived quantum potential is an additional degree of freedom where the structuring of intrinsic information takes place by negentropic action from the microscopically random quantum-thermal fluctuations. Such functional fluctuations provide a way for intentionality to come in from spontaneous ordering, leading to path selection as an instruction to act. The resultant intentionality becomes part of information-based action when functional interactions are selected and boundary conditions change, causing interference pattern matching through temporal re-organization of informational redundancy structures (not used in functional interactions). The self-referential dynamic structures (of evolving informational holons) transform syntac-tic structures into experienceable forms. In comparing the interference patterns of functional interactions during restructuring informational redundancy structures, the functionality of multiscale complexity as functional systems patterns gives experienceable forms the potential to understand “meaning” by reducing uncertainty in the process of structuring intrinsic information. The self-reference principle establishes dynamical pathways from the microscale to the macroscale (this includes nonlocal pathways), in which diachronic causation and how the disunity of causal order in the redundancy creates a weak unity of consciousness through its temporal structure, which has an inferred purpose that gives rise to a sense of self.

Advanced absorbing boundaries for elastodynamic finite element analysis: The added degree of freedom method

Absorbing boundaries are essential in engineering simulations, especially for elastodynamic problems, to ensure accuracy, reliability and numerical stability. In this paper, the added degree of freedom method (ADM) is developed as a novel approach to address absorbing boundary challenges in finite element analysis. In ADM, additional degrees of freedom (DOFs) are introduced within the absorbing domain to attenuate outgoing elastic waves. For the proposed ADM to implement the absorbing boundary, the stiffness and mass properties of both the added DOFs and conventional DOFs within the absorbing domain are adjusted. This adjustment aims to reduce the propagation speed of elastic waves within the medium, and to prolong the duration of interaction between elastic waves and the surrounding medium. Consequently, the vibrations of nodes can be effectively attenuated by applying damping forces to the added DOFs. The numerical results show that the ADM has the ability to absorb one-dimensional and two-dimensional elastic waves across a broad range of frequencies. Therefore, the proposed ADM offers an innovative solution for modeling absorbing boundaries in various scientific and engineering applications, addressing the challenges of simulating wave propagation within finite computational domains.

A magnetically actuated dynamic labyrinthine transmissive ultrasonic metamaterial

Currently, space-coiling acoustic metamaterials are static, requiring manual reconfiguration for sound-field modulation. Here, we introduce an approach to enable active reconfiguration, using standalone dynamic space-coiling unit cells called dynamic meta-bricks. Unlike their static counterparts, these meta-bricks, house an actuatable soft robotic-inspired magnetorheological elastomeric flap. This flap operates like a switch to directly control the transmitted ultrasound. For scalability, we present a hybrid stacking method, which vertically combines static and dynamic meta-bricks. This allows us to form a surface-integrated metasurface through concatenating variations of either fully static or hybrid stacks. By actuating dynamic metasurface sections, we experimentally demonstrate accurate modulation of λ/4 (≈2 mm) between two acoustic twin traps. We shift a levitated bead between the traps, validating that full-array operational dynamicity is achievable with partial, localised actuation. This work showcases the synergy between active and passive reconfigurability, opening possibilities to develop multifunctional metamaterials with additional degrees of freedom in design and control.

Three-dimensional spatial orbital angular momentum holography

The degree of freedom of orbital angular momentum of light has been used as a new information carrier in optical holographic information processing technology. However, current research on orbital angular momentum holography mainly focuses on two-dimensional orbital angular momentum holography, where the reconstructed two-dimensional holographic image is located in a certain plane in three-dimensional space. How to further implement three-dimensional spatial orbital angular momentum holographic technology and use it to increase the information capacity of holographic communication is still a blank. Here, we implement three-dimensional spatial orbital angular momentum holographic technology based on the degrees of freedom of orbital angular momentum and the positional degrees of freedom of reconstructed two-dimensional images in three-dimensional space. In other words, in the three-dimensional spatial orbital angular momentum holography, the acquisition of the target object image requires not only the correct orbital angular momentum state used for decoding, but also the correct spatial position where the object’s image is detected. In addition, we further investigate the three-dimensional spatial orbit angular momentum holographic multiplexing technology and point out that this multiplexing technology can be used for information encryption. Compared with traditional two-dimensional orbital angular momentum holography, three-dimensional spatial orbital angular momentum holography uses an additional degree of freedom. Therefore, the encryption scheme based on three-dimensional spatial orbital angular momentum holographic technology can further improve the security level of information. Our simulation results and experimental results have verified the feasibility of three-dimensional spatial orbit angular momentum holographic technology and three-dimensional spatial orbit angular momentum holographic encryption technology.