Ultimate Theory Research Articles

Upper bound solution of the vertical bearing capacity of the pile-bucket composite foundation of offshore wind turbines

Pile-bucket composite foundations are regarded as a promising solution for offshore wind power infrastructure. However, accurately assessing their vertical ultimate bearing capacity remains a technical challenge. Therefore, establishing an upper bound solution of the ultimate bearing capacity of the composite foundations is of significant importance for their promotion and application. This study begins with small-scale model tests, using Abaqus for modeling based on the relevant test conditions. Next, following model validation, the vertical bearing capacity of the composite foundations under different H/D ratios and the corresponding soil failure modes are investigated. According to the upper limit method and the ultimate equilibrium theory, the kinematic velocity field is subsequently constructed to derive the upper bound solution of the vertical bearing capacity. Finally, the effectiveness and accuracy of the proposed theoretical upper bound solution are verified against the results of model tests, and this study hopes to provide a reference for the future design of vertical bearing capacity of pile-bucket composite foundations.

Design of improved multi-cell L-shaped CFST columns under compression and bending

In recent years, there has been a notable surge in proposals for various forms of special-shaped concrete-filled steel tubular (CFST) columns. Despite various methods developed by researchers for determining the bearing capacity of multi-cell special-shaped CFST columns under different loading conditions, these methods remain lack unified. In this study, FE models were developed to simulate performances of improved multi-cell L-shaped CFST (ML-CFST) column under compression and bending. Parametric analyses have been performed to evaluate impact of various factors, including steel yield strength fy, compressive strength of concrete fcu, steel thickness t, loading direction θ, web height c, and axial load ratio n, on performances of ML-CFST columns. The findings of study indicate that the unidirectional flexural capacity of ML-CFST member exhibits a nearly linear relationship with the variables of t, fy, and c, with a minimal impact observed from fcu on flexural capacity. The width of extended section b, fcu, fy, and t have a certain effect on flexural capacity at any angle, particularly fy, t, and b. While fcu, fy, and t exert some influence on N/Nu-M/Mu correlation curves, their influences are marginal compared to the loading direction, which is the predominant influencing factor. Additionally, Mx0/Mπ/4-My0/M3π/4 curves gradually protrude outward with the increase in n. The effects of t, fy, and fcu on the shape of Mx0/Mπ/4-My0/M3π/4 curve were relatively insignificant. Simplified unidirectional flexural capacity calculation models were proposed based on stress analysis of cross-section under ultimate states. Given that flexural capacities estimated by simplified calculation model are slightly conservative, it is recommended to increase the flexural capacities by 10 %. Furthermore, an elliptical equation was formulated to predict the flexural capacity at any angle, with the predictions being slightly conservative. Based on ultimate equilibrium theory, a simplified calculation method was presented to predict unidirectional eccentric bearing capacities of ML-CFST columns. Through regression analysis, a simplified calculation method expressed as polar coordinate form for biaxial eccentric bearing capacity was established, with calculated values aligning well with FE results.

On the Aether Dynamics, Twin Paradox, and Ultimate Relativity of Solar Flares

In our previous work, Theory of Everything, we addressed the longstanding twin paradox of special relativity by introducing the concept of Aether force dynamics, F(v). This was achieved through the recognition that Aether force is cumulative, encompassing the sum of all force increments required to accelerate a massive body to velocity v. Similarly, the time dilation experienced by twin 2, the moving twin, is a cumulative effect, involving all time dilation increments accrued during their journey. This contrasts with the Lorentz contraction and mass dependence, which are instantaneous effects. Our approach successfully unified special and general relativity, extending the latter's focus on gravitational accelerations to incorporate any form of acceleration, thus leading to what we term the Ultimate Theory of Relativity. We have also applied this framework to describe dynamic processes in solar flares, drawing an analogy to the cinema problem, which involves maximizing the angle subtended by an observer to a screen. As in the twin paradox, the analysis necessitates the consideration of potential infinities, achieved by dividing finite quantities by zero or zero by zero. Remarkably, this led to a simultaneous application of Ultimate Relativity to both the cinema problem and solar flare dynamics, revealing that acceleration approaching infinity, a=1, is central to understanding these phenomena.

New Physics in the 3-3-1 models

The fundamental basics of the Standard Model such as local gauge symmetry and mass generation via the Higgs mechanism are widely confirmed by current experimental data. However, some problems such as neutrino masses, dark matter, baryon asymmetry of Universe have clearly indicated that the Standard Model cannot be the ultimate theory of Nature. To surpass the mentioned puzzles, many extensions of the Standard Model (called beyond Standard Model) have been proposed. Among beyond Standard Models, the 3-3-1 models have some intriguing features and they get wide attention. The pioneer models develop in some directions. In this paper, some versions of the 3-3-1 models and new consequences are presented.

Perspective on Coupled-cluster Theory. The evolution toward simplicity in quantum chemistry.

Coupled-cluster theory has revolutionized quantum chemistry. It has provided the framework to effectively solve the problem of electron correlation, the main focus of the field for over 60 years. This has enabled ab initio quantum chemistry to provide predictive quality results for most quantities of interest that are obtainable from first-principle calculations. The best that one can do in a basis is the 'full CI,' the exact solution of the non-relativistic Schrödinger equation or, if need be, the relativistic Dirac equation. With due regard to converging the basis set and adequate consideration of higher clusters and relativity in a calculation, virtually predictive results can be obtained. But in addition to its numerical performance, coupled-cluster theory also offers a conceptually new, many-body foundation for the theory that should be appreciated by all practitioners. The latter is emphasized in this perspective, leading to the 'evolution toward simplicity' in the title. The ultimate theory will benefit from the several features that are uniquely exact in coupled-cluster theory and its equation-of-motion (EOM-CC) extensions.

Testing theories of gravitation with the Interstellar Probe Radio Experiment

General Relativity (GR) will soon celebrate its 110th birthday, holding up against all experimental enquiry. Nonetheless, unification theories attempting to quantize gravity, such as string theory, are gaining footing. These hypothesize additional scalar, vector, and tensor long-range fields that couple to matter (Will, 2014), introducing violations to GR. Although such violations have never been detected, it is likely that GR will not be the ultimate theory of gravity. What is certain is that gravity tests are alive and well, pushing the validity of GR to new scales and accuracies, or -potentially- suggesting alternative routes for new physics.Building upon the legacy of Voyager and Pioneer missions, which demonstrated the capability to survive in the outer reaches of the solar system, the Interstellar Probe mission concept (McNutt et al., 2022) aims to characterise our heliosphere through state-of-the-art instrumentation, opening new frontiers also for GR testing. In this work, we investigate the possibility of constraining the Nordtvedt parameter η and the mass of the graviton via the Compton wavelength λC, by simulating the processing of 10 years of radiometric data from the Interstellar Probe. Station calibration and clock synchronisation, as well as limiting spacecraft precession manoeuvres are highlighted as key strategies for obtaining high-quality estimates. In the most favourable scenario, η can be constrained to less than 1.5·10-5, reducing the uncertainty obtained via Lunar Laser Ranging (Hofmann and Müller, 2018), and a lower bound of 1.4·1014 km is set for λC, improving the estimates obtained from planetary ephemerides (Bernus et al., 2020) and gravitational wave detection (Abbott et al., Jun 2021). Extending ranging measurement acquisition to 20 years improves the results tenfold. This experiment interrogates fundamental physics from a unique dynamical setting, investigating possible violations of the Equivalence Principle (EP) underlying GR.

Calculation of axial compression performance and bearing capacity of hollow sandwich glass fiber-reinforced polymer-concrete-steel double-skin tubular column

To evaluate the axial compressive performance of the hollow sandwich GFRP-concrete-steel double-skin tubular columns (DSTC), 15 composite column specimens were produced to study the effect of various design variables. And the study presents a rational and accurate finite element (FE) model that provides a detailed working mechanism of the DSTCs, leading to the enrichment of parametric research and the creation of an extensive database. Based upon the unified strength theory of double shear, limit equilibrium theory, and superposition theory, the study evaluates and compares the effectiveness of different bearing capacity calculation models. With each added millimeter in the thickness of the GFRP tube, the ultimate bearing capacity of the DSTC specimen increased by 23.6% and 61.8%, respectively, compared to that of the 1.5 mm thick GFRP tube sample. The lower the hollow ratio of the DSTC section, the higher its ultimate bearing capacity. Specimens with a hollow ratio of 0.3 and 0.43 showed an ultimate bearing capacity 1.4 times and 1.25 times higher, respectively, than those with a hollow ratio of 0.6. The study observes a relatively high level of precision in the results of the ultimate equilibrium theory, with an average error rate of 20%.

Luenberger compensator theory for heat-Kelvin-Voigt-damped-structure interaction models with interface/boundary feedback controls

Abstract An optimal, complete, continuous theory of the Luenberger dynamic compensator (or state estimator or state observer) is obtained for the recently studied class of heat-structure interaction partial differential equation (PDE) models, with structure subject to high Kelvin-Voigt damping, and feedback control exercised either at the interface between the two media or else at the external boundary of the physical domain in three different settings. It is a first, full investigation that opens the door to numerous and far reaching subsequent work. They will include physically relevant fluid-structure models, with wave- or plate-structures, possibly without Kelvin-Voigt damping, as explicitly noted in the text, all the way to achieving the ultimate discrete numerical theory, so critical in applications. While the general setting is functional analytic, delicate PDE-energy estimates dictate how to define the interface/boundary feedback control in each of the three cases.

Higgs-dilaton model revisited: Can a dilaton act as a QCD axion?

The Standard Model Lagrangian has an approximate scale symmetry in the high-energy limit. This observation can be included in the fundamental principle of the ultimate theory of Nature as the requirement of the exact quantum scale invariance. In this setup, all low-energy particle phenomenology can be obtained as a result of the spontaneous breaking of scale symmetry leading to the presence of the extra massless scalar field -- the dilaton. We explore the scenario in which this field is capable of solving the strong CP-problem in QCD in a similar way as in QCD axion models. The dilaton, playing the role of the axion, is coupled to the QCD sector and acquires a mass term due to non-perturbative breaking of scale symmetry. We show that the dilaton can form dark matter after the low-scale inflation. As a proof of concept, we construct a model of Higgs-driven inflation consistently realising the axion-like dilaton dark matter production compatible with the CMB data.

Adaptive droop control design with overcurrent protection for onboard DC microgrids in hybrid electric aircrafts

In this paper, an adaptive nonlinear droop-based control approach is proposed for converter-based self-contained electrical power systems (EPS) designed for electric aircraft applications to ensure tight voltage regulation and accurate load power distribution among parallel sources. By taking into account the accurate nonlinear dynamic models of the power converters, we mathematically prove an upper bound for the input current of each converter separately by means of Lyapunov methods and ultimate boundedness theory. In particular, the adopted nonlinear droop-based controller introduces a virtual voltage and a virtual resistance in series with the inductance and parasitic resistance of each DC/DC boost converter. To verify the proposed controller performance and its underlying developed theory, simulation results of the low-voltage bus dynamics have been presented for an onboard aicraft DC microgrid (MG).

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing Nature. The origin of scales, such as the Higgs vacuum expectation value (vev), may result from the spontaneous breakdown of the conformal symmetry by the dilaton field. In this work, we study whether this classical setup can be implemented in quantum theory and be phenomenologically viable by presenting an explicit construction where the exact conformal symmetry can be preserved and is anomaly free while being spontaneously broken. Not only the Higgs mass but also the genuine quantum scales like the QCD confinement radius are generated by the dilaton vev. We also discuss the extension of these ideas to the theories with dynamical gravity and show that the only finite subgroup of the local Weyl transformations which is anomaly free corresponds to the global scale symmetry. This means that the conformal invariance of the flat space theory is explicitly broken down to the scale symmetry by gravitational effects related to the Weyl anomaly.

Key Design Parameters Analysis and Calculation Theory Research on Bending Performance of Steel–UHPC Lightweight Composite Deck Structure

This paper aims to study the influence of key design parameters (e.g., reinforcement ratio, cover thickness, stud spacing, and thickness of the ultra-high-performance concrete (UHPC) layer) on the longitudinal and transverse bending performance, as well as the cracking load and ultimate bearing capacity calculation theory of steel–UHPC lightweight composite deck (LWCD) structure. Four transverse bending tests and four longitudinal bending tests on steel–UHPC composite plates and steel–UHPC composite beams were conducted, respectively. The refined finite element models of components with different key design parameters based on ABAQUS were established. The influences of different key design parameters on the transverse and longitudinal flexural behaviors (e.g., load-mid-span displacement curve, cracking stress, stiffness, elastic limit load, critical slip load, ultimate bearing capacity and ductility) were compared and analyzed in detail. The ultimate bearing capacity can be improved by increasing the thickness of UHPC layer and the reinforcement ratio of longitudinal reinforcement, and reducing the cover thickness and the spacing of studs. According to the longitudinal bending characteristics of the steel–UHPC lightweight composite deck structure, the calculation formulas for the cracking load and the ultimate bearing capacity of the steel–UHPC composite beam are proposed, and the calculated values are in good agreement with test results (the errors are basically within 10%), which is convenient for practical engineering applications.

Stability Analysis of Filled-Slope Reinforced by Frame with Prestressed Anchor-Plates under Static Action

Because of the current situation where the stability research of filled-slope reinforced by a frame with prestressed anchor-plates lags behind the actual engineering application, based on the ultimate balance theory, the calculation formulas of stability factor under the four arc slip surface of filled-slopes reinforced by a frame with prestressed anchor-plates are derived by using the improved Bishop method; the corresponding search method of the most dangerous slip surface is given and the calculation formulas of the pullout force of anchor-plates are improved. Based on two examples, the stability results calculated by the proposed algorithm are compared with those calculated by PLAXIS 3D and GeoStudio 2012 finite element software, and the following conclusions are drawn. (1) The improved pullout force of anchor-plates takes into account the friction of the front and rear surface of the anchor-plate and the effect of cohesion of fill soil in the passive earth pressure on the front end of the anchor-plate, which makes the force of the anchor-plate more complete. (2) The stability factor of example 1 calculated by this method differs from the results simulated by PLAXIS 3D and GeoStudio 2012 by 4.6% and 7.1%, respectively; the stability factor of example 2 calculated by this method differs from the results simulated by PLAXIS3D and GeoStudio 2012 by 3.2% and 4.5%, respectively, which can meet the engineering requirements. (3) The stability analysis method of filled-slope reinforced by a frame with prestressed anchor-plates that is proposed is reasonable and suitable for any arc slip surface in the filled-slope reinforced by a frame with prestressed anchor-plates, and it provides some guiding values for the design of practical engineering.

A power consensus controller with overvoltage protection for meshed DC microgrids

A novel distributed power consensus control approach with overvoltage protection is proposed and analysed for meshed direct current (DC) microgrids (MGs) with constant power loads (CPLs). The DC MG considered herein consists of source and load nodes connected over an undirected weighted graph induced by the electrical circuit network, namely the conductance matrix. When deploying, the proposed controller features a second graph, that models the communication network over which the source nodes exchange information such as the instantaneous powers, and which is used to adjust the power injection accordingly to achieve power sharing. Additionally, one aims to maintain the voltage at each source below operator-set limits. This feature is critical given the power and voltage dependency. By addressing the occurrence of abnormal voltage values at different nodes in the network, one would guarantee a relatively safer power consensus policy and microgrid operation. To accommodate both objectives, we developed a nonlinear power consensus-based control system, with a voltage-limiting component, by means of Lyapunov analysis and ultimate boundedness theory. Asymptotic closed-loop stability is also established around a set of equilibria. Finally, numerical simulations align with and validate our theoretical findings.

Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images.

This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is O(1/logt). Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition O(1/logt) of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images.

Deflection analysis of welded steel I‐girders with corrugated webs based on first yield

AbstractSinusoidal corrugated profile webs have been popularly used in steel structural designs to replace the flat webs in conventional welded beams, while there are better performances in corrugated web beams (CWBs) regarding more stability and less material used to against beam failures caused by buckling. Previous studies have provided that CWBs enabled numerous favourable benefits to be recognised as alternatives to the traditional weld beams in designing structures. Furthermore, as CWBs are proposed as the major load‐carrying elements, the maximum deflection in the elastic range is one of the important beam properties that should be precisely estimated and calculated. To find an appropriate method in computing the maximum deflection of CWBs based on the first yield for civil communities in Australia, proposed equations based on other standards will be employed to calculate the theoretical results for the comparisons with simulation‐based results. While applying the linear analysis simulations provided by SAP 2000, ultimate limit state design theory has also been used with requirements stated by AS 4100. In this study, the results in theoretical calculations and numerical simulations have been compared to conclude that the highly defined equations by ASTM [37] and Sause et al. [38] could precisely estimate the maximum deflections of CWBs based on the first yield in conjunction with requirements and limitations in Australian standards, which could be adequate for the structural design calculations in Australian design fields.

Magnetic field strength dependent SNR gain at the center of a spherical phantom and up to 11.7T.

PurposeThe SNR at the center of a spherical phantom of known electrical properties was measured in quasi‐identical experimental conditions as a function of magnetic field strength between 3 T and 11.7 T.MethodsThe SNR was measured at the center of a spherical water saline phantom with a gradient‐recalled echo sequence. Measurements were performed at NeuroSpin at 3, 7, and 11.7 T. The phantom was then shipped to Maastricht University and then to the University of Minnesota for additional data points at 7, 9.4, and 10.5 T. Experiments were carried out with the exact same type of birdcage volume coil (except at 3 T, where a similar coil was used) to attempt at isolating the evolution of SNR with field strength alone. Phantom electrical properties were characterized over the corresponding frequency range.ResultsElectrical properties were found to barely vary over the frequency range. Removing the influence of the flip‐angle excitation inhomogeneity was crucial, as expected. After such correction, measurements revealed a gain of SNR growing as B0 1.94 ± 0.16 compared with B0 2.13 according to ultimate intrinsic SNR theory.ConclusionsBy using quasi‐identical experimental setups (RF volume coil, phantom, electrical properties, and protocol), this work reports experimental data between 3 T and 11.7 T, enabling the comparison with SNR theories in which conductivity and permittivity can be assumed to be constant with respect to field strength. According to ultimate SNR theory, these results can be reasonably extrapolated to the performance of receive arrays with greater than about 32 elements for central SNR in the same spherical phantom.

Study on Static and Fatigue Behaviors of Steel-UHPFRC Composite Deck Structure.

Ultra-high-performance fiber-reinforced cementitious composite (UHPFRC) is used in orthotropic steel deck (OSD) to form a lightweight composite deck structure (LWCD), which is expected to solve the problems of fatigue cracking of traditional steel deck and pavement damage. This paper aims to study the influence of key design parameters on longitudinal bending and transverse fatigue performance, as well as the ultimate bearing capacity calculation theory of the LWCD. A local finite-element (FE) model was built to evaluate the vehicle-induced stress ranges of six typical fatigue-prone details. In total, eight negative bending tests on steel-UHPFRC composite beams and one fatigue test on a steel-UHPFRC composite plate were conducted to investigate the longitudinal bending performance and the transverse flexural fatigue behavior of the LWCD, respectively. The results show that adding a 60-mm UHPFRC layer can significantly reduce the stress amplitude of six typical fatigue details by 44.8% to 90%. The failure mode of the longitudinal bending tests is the U-rib buckle and all UHPFRC layers exhibit multiple cracking behaviors when the specimens failed. The longitudinal cracking stresses of the specimens are between 20.0 MPa to 27.3 MPa. The reinforcement ratio and cover thickness have a great influence on the cracking stress. While the ultimate bearing capacity of specimens with different parameters has little difference. The calculation method of the ultimate bearing capacity of a steel-UHPFRC composite structure is proposed. When the strain at the bottom of the u-rib is taken as 1.2 times the design yield strain, the calculated results are in good agreement with the experimental results. No fatigue failure was observed after 66.12 million fatigue cycles under the design load, highlighting the favorable fatigue resistance of the proposed LWCD.

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts)

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?

A 32-element loop/dipole hybrid array for human head imaging at 7T.

To improve whole-brain SNR at 7Tesla, a novel 32-element hybrid human head array coil was developed, constructed, and tested. Our general design strategy is based on 2 major ideas: Firstly, following suggestions of previous works based on the ultimate intrinsic SNR theory, we combined loops and dipoles for improvement of SNR near the head center. Secondly, we minimized the total number of array elements by using a hybrid combination of transceive (TxRx) and receive (Rx) elements. The new hybrid array consisted of 8 folded-end TxRx-dipole antennas and 3 rows of 24 Rx-loops all placed in a single layer on the surface of a tight-fit helmet. The developed array significantly improved SNR in vivo both near the center (∼20%) and at the periphery (∼20% to 80%) in comparison to a common commercial array coil with 8 transmit (Tx) and 32 Rx-elements. Whereas 24 loops alone delivered central SNR very similar to that of the commercial coil, the addition of complementary dipole structures provided further improvement. The new array also provided ∼15% higher Tx efficiency and better longitudinal coverage than that of the commercial array. The developed array coil demonstrated advantages in combining complementary TxRx and Rx resonant structures, that is, TxRx-dipoles and Rx-loops all placed in a single layer at the same distance to the head. This strategy improved both SNR and Tx-performance, as well as simplified the total head coil design, making it more robust.