Global Isotropy Research Articles

Advancing sustainable construction through innovative transparent wood composite structures with enhanced functionalities

Advancements in transparent wood materials hold immense promise for eco-friendly construction, combating resource depletion, and enhancing energy efficiency. Yet, the quest for versatility and global uniformity poses challenges. Enter our breakthrough: a three-layer transparent wood that integrates thermal energy storage. We achieved this by compressing three partially impregnated wood substrates, featuring a silica-stabilized polyethylene glycol (PEG) core flanked by two polymethyl methacrylate (PMMA) layers. In pursuit of optical and mechanical perfection, we employed a multi-layer approach to ensure global isotropy. Morphological analysis unveiled compact, hierarchical structures in the core, PEG encapsulation, and an innovative solution for preventing leaks, culminating in a remarkable latent heat of 15.0 J/g and superior thermal stability. Optical testing reported outstanding properties, with an optical transmittance of 45 % and a haze of 76 % at 800 nm. Our design featuring crossed-lamination not only achieved isotropic light distribution but also improved mechanical consistency and water resistance. Notably, our environmentally-simulated tests showcased remarkable thermal insulation properties, credited to a low thermal conductivity (0.34 W/mK) surpassing traditional glass, as well as phase-change functionality. Our pioneering multilayer transparent wood stands to revolutionize energy-efficient construction and elevate indoor thermal comfort.

Design of isotropic 2D chiral metamaterials based on monohedral pentagonal tessellations

A novel class of transversely-isotropic metamaterials with the potential to exhibit a wide range of Poisson’s ratios and stiffnesses is proposed in this work. These metamaterials, which also have the potential to exhibit auxetic behaviour, are formed through the chiralisation of 2D monohedral Euclidean pentagonal tessellations. Through Finite Element simulations and experimental testing on additively manufactured prototypes, we show that these systems can exhibit Poisson’s ratios which encompass the entire range of transverse isotropicity, i.e. +1 to -1, and that the mechanical properties of these structures can be tailored considerably through variation of the geometric parameters without a loss of global symmetry and isotropy. The level of versatility observed in these new metamaterials exceeds by far that which is commonly found in traditional and well-known isotropic auxetic systems such as hexachiral honeycombs. In addition, analytical expressions pertaining to the geometric limits which define the realisability of this new class of auxetic metamaterials have also been derived and presented. The findings of this work demonstrate that pentagonal tessellations have considerable potential for the development of novel metamaterials and that the geometric constraints associated with transverse isotropy need not necessarily be an insurmountable barrier for the design of metamaterials with tailorable and versatile mechanical properties.

A novel hand exoskeleton to enhance fingers motion for tele-operation of a robot gripper with force feedback☆

This research describes a robotic system's design, optimization, and implementation processes for tele-operation with haptic feedback using the Hand Exoskeleton of New technologies research center (HEXON) as a novel haptic mechanism and the HEXON robotic gripper to work collaboratively with the exoskeleton. In particular, a force-sensitive robotic gripper is connected to a hand exoskeleton, mimics the user's hand movements, and transfers haptic feedback through the exoskeleton. The two-finger exoskeleton's design process consists of a multi-criteria optimization procedure to simultaneously maximize applied force to the finger and workspace of the attached exoskeleton, optimizing both the Perpendicular Impact Force (PIF) and the Global Isotropy Index (GII), considering worst-case collision avoidance. Due to the tele-operation application and using a robotic arm as a slave in the remote scenario, the gripper can be used as an end-effector for a palletizing 3-DOF robotic arm, and movement of the gripper can be achieved by using a visual sensor to pinpoint the user's hand location in 3D space. With the aim of the stress analysis software, the exoskeleton and gripper designs were analyzed to evaluate the system strength against applied forces. Finally, based on the achieved results, the gripper and two-fingered exoskeleton prototypes were fabricated. Simulations and experimental results are reported, showing the potential of the HEXON in haptics and tele-operation applications, and the exoskeleton is used to operate a robotic arm and gripper while the user can perceive the objects virtually.

Isotropy groups of free racks and quandles

In this paper, we characterize the (covariant) isotropy groups of free, finitely generated racks and quandles. As a consequence, we show that the usual inner automorphisms of such racks and quandles are precisely those automorphisms that are “coherently extendible”. We then use this result to compute the global isotropy groups of the categories of racks and quandles, i.e. the automorphism groups of the identity functors of these categories.

Structural design of a microsurgery-specific haptic device: neuroArmPLUSHD prototype

A microsurgery-specific haptic interface with articulated structure, possessing 3 active, 4 passive and 3 supplementary degrees of freedom (DOFs), was designed and developed. The system includes a 3-DOF active serial linkage design, mimicking the human upper extremity. It is combined with a microsurgery-specific end-effector, comprised of a 3-DOF passive gimbal mechanism and a 1-DOF passive exchangeable surgical toolset. The spherical gimbal workspace twinned with the larger linkage arm workspace allow accurate and delicate movements to maneuver the surgical tool in narrow corridors, corresponding to conventional surgery. The structural design of the device is based on kinematic performance measures aimed to enhance ergonomics and mitigate training limitations of novice end-users. A supplementary 3-DOF adjustable base further improved ergonomics for end-users of different sizes. Force feedback was provided to improve safety, i.e. avoidance of force errors in execution of surgical tasks. This haptic interface provides high positional and output force resolution (0.92–1.46 mm in Cartesian coordinate system and 0.2 N, respectively), wide range of allowable force (up to 15 N), high global manipulability (0.77), global isotropy (0.68) and stiffness (2.3 N/mm). The work, indeed, introduces a novel kinematic performance index, Dexterous Conditioning Index (DCI), based on the volume of dexterous workspace, correlating to ease of use and decreased singularity. Accordingly, the proposed haptic device demonstrates a high level of accuracy, haptic feedback, dexterous workspace, and performance, ideal for implementation in robot-assisted microsurgery.

Root Based Optimization Algorithm for Task-Oriented Structural Design of a Multi-Axial Road Test Rig

A novel root based optimization algorithm (ROA), which mimics the proliferation of plant roots, is proposed to evaluate the performances of a multi-axial road test rig over a prescribed workspace. Plant roots have developed complex behavior patterns to search for nutrients in the soil and even exhibit swarm intelligence. The growing roots can adapt their actions such as elongation, branching, and tropistic movement according to the environment. During the process of foraging for water and nutrients, the adaptive growth behavior of roots can be simulated to tackle the optimization problem. The efficiency of the proposed ROA has been validated by comparing it with well-known intelligent algorithms using classical and IEEE CEC 2019 benchmark functions. Computational results indicate that ROA outperforms other algorithms to search a global optimum on several benchmarks. Furthermore, the results are tested with nonparametric statistical methods, e.g., Wilcoxon rank-sum test. Besides, ROA is applied to the optimal dimensioning synthesis of the multi-axial road test rig (MRTR) based on the orthogonal 6-RSS parallel manipulator to promote the device's performance. The inverse kinematics of the multi-axial road test rig based on the asymmetrical orthogonal 6-RSS parallel mechanism is analyzed in detail. Applying the achieved dimensionless Jacobian, the performance criteria involving the global isotropy index, the force/velocity transmissibility index, the decoupling index are established. By simultaneously taking account the proposed criteria of performance, structural optimization is carried out resorting to ROA. Finally, a set of optimized dimensional parameters is obtained. The practical application further illustrates that ROA has the potential to deal with complex optimization problems.

Characterization of Turbulence in an Optically Accessible Fan-Stirred Spherical Combustion Chamber

ABSTRACT Fundamental characteristics of fan-generated turbulence inside a constant-volume combustion chamber (CVCC) with 400 mm inner diameter under high-pressure and high-temperature conditions have been investigated to establish benchmark data for studies of turbulent premixed flame propagation. Here, the CVCC was designed to withstand up to 1.0 MPa initial pressure and 600 K initial temperature and equipped with four fans oriented in a tetrahedron configuration. A time-resolved particle imaging velocimetry (TR-PIV) is employed to characterize the turbulence under various thermodynamic conditions. Additionally, stereoscopic TR-PIV measurements were conducted to characterize the three-dimensional turbulent flow field inside the chamber. The results showed that the chamber could achieve homogenous and isotropic turbulence. A reasonably isotropic stationary turbulence with large turbulence intensities (up to ≈ 4.7 m/s) was achieved in the central region extending to almost 50 mm radius. This has been manifested by near-zero mean velocities and directional invariance of turbulence intensities. Global homogeneity and isotropy ratios in the chamber were close to unity, indicating weak anisotropy. The spectral energy spectra of the generated turbulent flow fields were in satisfactory agreement with the well-known Kolmogorov’s – 5/3 law associated with homogeneous isotropic turbulence irrespective of the intensity of the turbulence. Various spatio-temporal length scales characterizing the turbulent flow field including the integral, Taylor, and Kolmogorov length scales were reported. Turbulence statistics and inherent parameters were investigated at elevated pressure and temperature conditions as well as results from test cases to determine turbulent–flame propagation speeds were reported. Accordingly, the present canonical configuration apparatus can be conveniently adopted for several turbulent combustion studies including mainly the determination of turbulent burning velocity for gaseous and liquid premixed flames in nearly homogeneous isotropic turbulence.

Constructing the virtual fundamental class of a Kuranishi atlas

Consider a space $X$, such as a compact space of $J$-holomorphic stable maps, that is the zero set of a Kuranishi atlas. This note explains how to define the virtual fundamental class of $X$ by representing $X$ via the zero set of a map $S_M: M\to E$, where $E$ is a finite dimensional vector space and the domain $M$ is an oriented, weighted branched topological manifold. Moreover, $S_M$ is equivariant under the action of the global isotropy group $\Gamma$ on $M$ and $E$. This tuple $(M,E, \Gamma, S_M)$ together with a homeomorphism $S_M^{-1}(0)/\Gamma \to X$ forms a single finite dimensional model (or chart) for $X$. The construction assumes only that the atlas satisfies a topological version of the index condition that can be obtained from a standard, rather than a smooth, gluing theorem. However if $X$ is presented as the zero set of an sc-Fredholm operator on a strong polyfold bundle, we outline a much more direct construction of the branched manifold $M$ that uses an sc-smooth partition of unity.

Degenerate limits for one-parameter families of non-fixed-point diffusions on fractals

The Sierpinski gasket is known to support an exotic stochastic process called the asymptotically one-dimensional diffusion. This process displays local anisotropy, as there is a preferred direction of motion which dominates at the microscale, but on the macroscale we see global isotropy in that the process will behave like the canonical Brownian motion on the fractal. In this paper we analyse the microscale behaviour of such processes, which we call non-fixed point diffusions, for a class of fractals and show that there is a natural limit diffusion associated with the small scale asymptotics. This limit process no longer lives on the original fractal but is supported by another fractal, which is the Gromov–Hausdorff limit of the original set after a shorting operation is performed on the dominant microscale direction of motion. We establish the weak convergence of the rescaled diffusions in a general setting and use this to answer a question raised in [14] about the ultraviolet limit of the asymptotically one-dimensional diffusion process on the Sierpinski gasket.

Design and Evaluation of a Haptic Interface With Octopod Kinematics

The study of human motor control using functional magnetic resonance imaging gives rise to many challenges. One of them is the design of haptic interfaces that are compatible with the magnetic field. To achieve this, the existing haptic interfaces employ parallel kinematics. However, they are limited to three degrees of freedom (DOFs). When trying to offer more DOF without floating actuators, parallel kinematics suffer from direct kinematic singularities, and thus, strong mechanical anisotropy. In this paper, we determine an optimal six DOF kinematics that overcomes these limitations. To this end, we use performance indices such as singularity occurrence, worst case output capabilities, sensitivity, and the global isotropy index. The resulting Octopod kinematics avoids a range of direct kinematic singularities by design. Finally, we pre-sent and evaluate a non-magnetic-resonance-compatible prototype of this novel type of kinematics.

Preoperative optimization of the surgical robot considering internal diversity of workspace

Surgical robots have increased in popularity, and their performance is closely related to the robotic positioning before surgery. Many recent studies in preoperative planning have focused on the pose selection of the robot and the port placement. However, it is difficult to position the surgical robot simply based on experience. To solve this problem, the surgical workspace is subdivided into several subspaces with different weights. Global isotropy index and cooperation capability index are proposed to reflect the performance of the surgical robot and used as optimization functions. Particle swarm optimization is used to optimize the setup parameters. Based on different weight distributions, setup parameters can be automatically given and sent to the simulation system to display the setup and guide the robot positioning. The results show that the setup optimization considering the internal diversity of workspace is capable of satisfying the detailed requirements of robotic surgery and effectively guide the robotic surgery setup.

Design optimization of 3PRS parallel manipulator using global performance indices

This paper presents an optimal kinetostatic design method for a general 3PRS (Prismatic-revolute-spherical) spatial parallel manipulator by formulating a multi-objective optimization problem considering the performance indices are as the objective functions. Three performance criteria—Global conditioning index (GCI), Global stiffness index (GSI) and workspace volume-were formulated and the effect of actuator layout angle on the performance indices was studied. A multi-objective evolutionary algorithm based on the Control elitist non-dominated sorting genetic algorithm (CENSGA) was adopted to find the final approximation set. The optimal geometric parameters that yield minimal compliance with larger workspace volume and improved dexterity are suggested for a general 3PRS parallel manipulator. For the optimal design, it is shown that global isotropy and global stiffness of the platform is improved at the cost of workspace reduction.

Jacobian Matrix Normalization - A Comparison of Different Approaches in the Context of Multi-Objective Optimization of 6-DOF Haptic Devices

This paper focuses on Jacobian matrix normalization and the performance effects of using different criterion and techniques. Normalization of the Jacobian matrix becomes an issue when using kinematic performance indices and the matrix contains elements with non-homogenous physical units, i.e. representing both translational and rotational motions. Normalization is necessary in multi objective optimization if kinematic performance indices are used based on the full Jacobian matrix. Different methods have been proposed in literature for defining a scaling factor used to normalize the Jacobian. Based on a comparison of a few of these methods, we conclude that it is better to have the scaling factor as a design variable in the multi objective optimization. However, as an alternative, a new scaling factor is proposed based on the relationship between linear actuator motion range in joint space and rotational end effector motion in task space, a proposal underpinned by simulation, analysis and comparison of optimization results using existing normalization techniques. For optimization, performance indices for workspace, kinematic sensitivity, device isotropy and inertia are considered. To deal with the multi-objective optimization problem, genetic algorithms are employed together with a normalized multi-objective optimization function. The performances of different device configurations (depending on the normalization method and the global isotropy index used) are presented in this article.

Synthesis of k<SUP align="right">th</SUP> order fault-tolerant kinematically redundant manipulator designs using relative kinematic isotropy

Fault tolerance has become an essential capability in manipulator design methodologies as robotic manipulation systems are more frequently employed in hazardous environments and on geometrically complex or heavy duty industrial operations, where mechanical joint failures are likely to occur. This work focuses on the development of a redundant manipulator design methodology aimed at minimising the degradation in manipulator performance quality that results from k arbitrary joint failures. The relative weighted global isotropy index (RWGII) is developed for use as a manipulator design fitness metric. This metric takes into account the primary manipulation goal of maintaining kinematic dexterity, the secondary goals of collision avoidance and torque minimisation, and fault tolerance capability. The genetic algorithm search of an immense manipulator design space, conducted using the new fault-tolerant manipulator design fitness metric, yields redundant manipulator designs that effectively minimise fault susceptibility due to k joint failures while maintaining dexterous, redundancy-resolved motion on specific tasks.

Micro-scale experimental investigation of the swelling anisotropy of the Callovo-Oxfordian argillaceous rock

AbstractAn experimental study of the swelling anisotropy of the Callovo-Oxfordian argillaceous rock under hydration is presented. The investigation, which combines environmental scanning electron microscopy (ESEM) and digital image correlation techniques, has been carried out at the micrometric scale of the composite microstructure of the rock. Specimens were hydrated in the ESEM over a wide range of relative humidity and observations conducted on two planes: plane 1 parallel to the bedding plane, and plane 2 perpendicular to it. The observations reveal that the local swelling (which can be quantified at a local gauge length of about 5 μm) is strongly anisotropic in both planes. The global swelling, measured over areas of about 500 μm in width, is also clearly anisotropic in plane 2 (with major swelling direction normal to the bedding plane), but not in plane 1. The global isotropy in plane 1 arises from the uniform distribution of the orientation of anisotropic local strains, while the anisotropic swelling in plane 2 is due to a preferred local orientation.

Particle image velocimetry study of fractal-generated turbulence

AbstractAn experimental investigation involving space-filling fractal square grids is presented. The flow is documented using particle image velocimetry (PIV) in a water tunnel as opposed to previous experiments which mostly used hot-wire anemometry in wind tunnels. The experimental facility has non-negligible incoming free-stream turbulence (with 2.8 % and 4.4 % in the streamwise (${u}^{\ensuremath{\prime} } / U$) and spanwise (${v}^{\ensuremath{\prime} } / U$) directions, respectively) which presents a challenge in terms of comparison with previous wind tunnel results. An attempt to characterize the effects of the incoming free stream turbulence on the grid-generated turbulent flow is made and an improved wake-interaction length scale is proposed which enables the comparison of the present results with previous ones for both fractal square and regular grids. This length scale also proves to be a good estimator of the turbulence intensity peak location. Furthermore, a new turbulence intensity normalization capable of collapsing${u}^{\ensuremath{\prime} } / U$for various grids in various facilities is proposed. Comparison with previous experiments indicates good agreement in turbulence intensities, Taylor microscale, as well as various other quantities, if the improved wake-interaction length scale is used. Global and local isotropy of fractal-generated turbulence is assessed using the velocity gradients of the two-component (2C) two-dimensional (2D) PIV and compared with regular grid results. Finally, the PIV data appear to confirm the new dissipation behaviour previously observed in hot-wire measurements.

Effective action approach to cosmological perturbations in dark energy and modified gravity

In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, δGμν = 8πGδTμν+δUμν for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of δUμν for two explicit generic examples: (i) the dark sector does not contain extra fields, ℒ = ℒ(gμν) and (ii) the dark sector contains a scalar field and its first derivative ℒ = ℒ(gμν,ϕ,∇μϕ). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.

Source characterization and modeling development for monoenergetic-proton radiography experiments on OMEGA

A monoenergetic proton source has been characterized and a modeling tool developed for proton radiography experiments at the OMEGA [T. R. Boehly et al., Opt. Comm. 133, 495 (1997)] laser facility. Multiple diagnostics were fielded to measure global isotropy levels in proton fluence and images of the proton source itself provided information on local uniformity relevant to proton radiography experiments. Global fluence uniformity was assessed by multiple yield diagnostics and deviations were calculated to be ∼16% and ∼26% of the mean for DD and D(3)He fusion protons, respectively. From individual fluence images, it was found that the angular frequencies of ≳50 rad(-1) contributed less than a few percent to local nonuniformity levels. A model was constructed using the Geant4 [S. Agostinelli et al., Nuc. Inst. Meth. A 506, 250 (2003)] framework to simulate proton radiography experiments. The simulation implements realistic source parameters and various target geometries. The model was benchmarked with the radiographs of cold-matter targets to within experimental accuracy. To validate the use of this code, the cold-matter approximation for the scattering of fusion protons in plasma is discussed using a typical laser-foil experiment as an example case. It is shown that an analytic cold-matter approximation is accurate to within ≲10% of the analytic plasma model in the example scenario.

Optimal transseptal puncture location for robot‐assisted left atrial catheter ablation

The preferred method of treatment for atrial fibrillation (AF) is by catheter ablation, in which a catheter is guided into the left atrium through a transseptal puncture. However, the transseptal puncture constrains the catheter, thereby limiting its manoeuvrability and increasing the difficulty in reaching various locations in the left atrium. In this paper, we address the problem of choosing the optimal transseptal puncture location for performing cardiac ablation to obtain maximum manoeuvrability of the catheter. We have employed an optimization algorithm to maximize the global isotropy index (GII) to evaluate the optimal transseptal puncture location. As part of this algorithm, a novel kinematic model for the catheter has been developed, based on a continuum robot model. Pre-operative MR/CT images of the heart are segmented using the open source image-guided therapy software, 3D Slicer, to obtain models of the left atrium and septal wall. These models are input to the optimization algorithm to evaluate the optimal transseptal puncture location. The continuum robot model accurately describes the kinematics of the catheter. Simulation and experimental results for the optimal transseptal puncture location are presented in this paper. The optimization algorithm generates discrete points on the septal wall for which the dexterity of the catheter in the left atrium is maximum, corresponding to a GII of 0.4362. We have developed an optimization algorithm based on the GII to evaluate the optimal position of the transseptal puncture for left atrial cardiac ablation.

Probing the anisotropic local Universe and beyond with SNe Ia data

The question of the transition to global isotropy from our anisotropic local Universe is studied using the Union 2 catalogue of Type Ia supernovae (SNe Ia). We construct a "residual" statistic sensitive to systematic shifts in their brightness in different directions and use this to search in different redshift bins for a preferred direction on the sky in which the SNe Ia are brighter or fainter relative to the 'standard' LCDM cosmology. At low redshift (z<0.05) we find that an isotropic model such as LCDM is barely consistent with the SNe Ia data at 2-3 sigma. A complementary maximum likelihood analysis of peculiar velocities confirms this finding -- there is a bulk flow of around 260 km/sec at z \sim 0.06, which disagrees with LCDM at 1-2 sigma. Since the Shapley concentration is believed to be largely responsible for this bulk flow, we make a detailed study of the infall region: the SNe Ia falling away from the Local Group towards Shapley are indeed significantly dimmer than those falling towards us and on to Shapley. Convergence to the CMB rest frame must occur well beyond Shapley (z>0.06) so the low redshift bulk flow can systematically bias any reconstruction of the expansion history of the Universe. At high redshifts z>0.15 the agreement between the SNe Ia data and the isotropic LCDM model does improve, however, the sparseness and low quality of the data means that LCDM cannot be singled out as the preferred cosmological model.