Kinematic Degrees Research Articles

Towards quantum gravity with neural networks: solving the quantum Hamilton constraint of U(1) BF theory

Abstract In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in principle applicable to this problem. We consider U(1) BF theory in three dimensions, quantised with loop quantum gravity methods. In particular, we formulate a master constraint corresponding to Hamilton and Gauß constraints using loop quantum gravity methods. To make the problem amenable for numerical simulation we fix a graph and introduce a cutoff on the kinematical degrees of freedom, effectively considering U q ( 1 ) BF theory at a root of unity. We show that the neural network quantum state ansatz can be used to numerically solve the constraints efficiently and accurately. We compute expectation values and fluctuations of certain observables and compare them with exact results or exact numerical methods where possible. We also study the dependence on the cutoff.

Towards quantum gravity with neural networks: solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit

Abstract The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U(1)3 BF- theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to Uq(1)3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann’s strategy and the Gauβ master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints.

Uniform stretching behavior of single crease origami arrays

Origami arrays featuring ideal purely rotational creases inherently possess multiple kinematic degrees of freedom. The incorporation of crease rotational stiffness introduces additional constraint relations to the kinematic morphology of the origami array, due to the interaction between the plate and the crease. This paper concentrates on elucidating the coupling effect, employing two theoretical models to systematically analyze the uniform stretch process of single crease origami arrays. The validity of our theoretical approaches is substantiated through verification in the finite element method. Firstly, the mechanical equations of the origami unit, together with the length and angle constraint equations of the origami array, are amalgamated to formulate a comprehensive set of morphological computational equations specific to the single crease origami array. This set enables the realization of morphological analysis for general origami arrays. Moreover, energy equations for the origami array are computed using an equivalent rigid plate nonlinear creasing element. When combined with constraint equations corresponding to horizontal stretch displacement, these energy equations contribute to the establishment of a nonlinear optimization framework for determining the morphology of uniform single crease origami arrays. Notably, our investigation reveals that during the early stages of the unfolding process for a single crease origami array, even a small relative horizontal stretch displacement can induce a drastic change in the center crease. Through finite element analysis of general origami arrays, it is shown that the proposed theoretical analysis method applies to different crease stiffness, both unfolding and folding processes, and different plate types. The research method in this paper can provide ideas for systematically analyzing the influence mechanism of crease properties on the morphological features of origami structures.

State-space dynamic inflow modelling for hovering rotors in fixed- and moving-ground effect

This paper's objective is to apply a novel identification technique to obtain a dynamic state-space wake inflow model accounting for the effects of a stationary/moving ground beneath a hovering rotor. The identification is based on a dataset of computational simulations (training set) provided by an in-house free-wake mid-fidelity solver. The evaluation of the wake contribution is optimised through a generalised mirror-image model to reduce the computational cost without losing accuracy. Stationary and moving ground effects are analysed and discussed in the present work, considering both parallel and inclined ground with respect to the rotor disk and heaving and pitching ground motion. The proposed state-space wake inflow model relates the inflow coefficients to a set of inputs, including the aerodynamic hub loads (akin to the well-known Pitt-Peters approach) and the kinematic degrees of freedom of the ground. For a number of rotor/ground configurations, the identified model is successfully validated against the simulations directly provided by the nonlinear, free-wake aerodynamic solver.

Effects of postural instability on the coordination between posture and arm reaching

Reaching from standing requires adjustments of hand movement and posture, which are assured by redundant kinematic degrees of freedom. However, the increased demand for postural adjustments may interfere with the stability of reaching. The objective of this study was to investigate the effect of postural instability on the use of kinematic redundancy to stabilize the finger and center-of-mass trajectories during reaching from standing in healthy adults. Sixteen healthy young adults performed reaching movements from standing with and without postural instability induced by small base-of-support. The three-dimensional positions of 48 markers were recorded at 100 Hz. The uncontrolled manifold (UCM) analysis was performed separately with the finger and center-of-mass positions being the performance variables, and joint angles being the elemental variables. ΔV, the normalized difference between the variance in joint angle that does not affect task performance (VUCM) and the variance that does affect task performance (VORT), was calculated separately for finger (ΔVEP) and center-of-mass (ΔVCOM) positions, and was compared between stable and unstable base-of-support conditions. ΔVEP decreased after movement onset and reached its minimum value at around 30–50% of the normalized movement time, and increased until movement offset, while ΔVCOM remained stable. At 60%–100% normalized movement time, ΔVEP was significantly reduced in the unstable base-of-support, compared to the stable base-of-support condition. ΔVCOM remained similar between the two conditions. At movement offset, ΔVEP was significantly reduced in the unstable base-of-support, compared to the stable base-of-support condition, and was associated with a substantial increase in VORT. Postural instability might reduce the ability to use kinematic redundancy to stabilize the reaching movement. The central nervous system may prioritize the maintenance of postural stability over focal movement when postural stability is challenged.

Identification of deformed configurations of segmental tunnel rings based on measured convergences

If convergences grow so large that the serviceability of a tubbing ring is lost, remedial measures must be taken. In this context, it is useful to reconstruct the displacement history of the tunnel ring in order to gain insight into the evolution of the structural behavior that has led to the current configuration. This challenge is tackled with the help of measured convergences and rigid body kinematics. The latter are sufficient, because the deformations of tubbings, resulting from normal forces and bending moments, do not contribute significantly to the displacements of segmental rings. The analysis is focused on convergences measured during a real-scale test of a symmetric tunnel ring. It consists of six tubbings and has three kinematic degrees of freedom. Deformed configurations are reproduced by optimizing the three scalar components of one symmetric and two antisymmetric modes of rigid body displacements. This problem is under-determined, because convergences are routinely measured in two directions only. Its solution is obtained in two steps. At first, the component of the symmetric mode of rigid body displacements is identified such that the measured convergences are reproduced in the best-possible fashion. Thereafter, the remaining differences between measured and modeled convergences are reduced to zero by optimizing the components of the two antisymmetric modes. This kind of structural analysis starts with the most recent set of measured convergences. It proceeds, in a step-by-step manner backwards in time to older sets of monitored data. It is shown that the developed method allows for a satisfactory reproduction of the displacement history of the tested tubbing ring, making use of measured vertical and horizontal convergences. The obtained visualization of the displacement history of the entire tunnel ring provides more insight into the structural behavior than diagrams showing only the evolution of single convergences.

A Method for Designing Multi-Layer Sheet-Based Lightweight Funicular Structures

Multi-layer spatial structures usually take considerable external loads with a small material usage at all scales. Polyhedral graphic statics (PGS) provides a method to design multi-layer funicular polyhedral structures, and the structural forms are usually materialized as space frames. Our previous research shows that the intrinsic planarity of the polyhedral geometries can be harnessed for efficient fabrication and construction processes using flat-sheet materials. Sheet-based structures are advantageous over conventional space frame systems because sheets can provide more load paths and constrain the kinematic degrees of freedom of the nodes. Therefore, they are more capable of taking a wider variety of load cases compared to space frames. Moreover, sheet materials can be fabricated into complex shapes using CNC milling, laser cutting, water jet cutting, and CNC bending techniques. However, not all sheets are necessary as long as the load paths are preserved and the system does not have kinematic degrees of freedom. To find an efficient set of faces that satisfies the requirements, this paper first incorporates and adapts the matrix analysis method to calculate the kinematic degrees of freedom for sheet-based structures. Then, an iterative algorithm is devised to help find a reduced set of faces with zero kinematic degrees of freedom. To attest to the advantages of this method over bar-node construction, a comparative study is carried out using finite element analysis. The results show that, with the same material usage, the sheet-based system has improved performance than the framework system under a range of loading scenarios.

Kirigami tiled surfaces with multiple configurations

This paper presents new kirigami patterns consisting oftilesconnected bysub-foldsthat can approximate multiple specified target surfaces. The curvature of the surfaces approximated by the tiles varies as the patterns are folded, allowing access to a wide range of curvatures. A numerical framework is developed for the synthesis of the fold patterns that approximate a given set of target surfaces. The pattern synthesis process is framed as a tile placement problem, where compatible tile arrangements associated with each target surface are computed by solving a constrained optimization problem. After computing a set of tile arrangements, sub-folds are added to connect adjacent tiles. The resulting patterns are rigid foldable with many kinematic degrees of freedom, allowing them to achieve configurations that approximate the specified target surfaces. Kinematic simulations verify the existence of continuous paths between the target surfaces. A prototype pattern with six target surfaces is fabricated using three-dimensional printed components.

Orientational-induced strain hardening of axisymmetric grains

The rheological response of oriented axisymmetric grains has additional degrees of complexity associated with their microstructure orientation. These additional kinematic degrees of freedom that give rise to complex transient macroscale rheological responses are not well understood. In this Letter, we study the rheology of axisymmetric grains subjected to transient flow. We identify strong coupling between the microstructure rearrangement and strain hardening which, under certain conditions, can yield jamming. We identify the critical conditions corresponding to jamming and the dependency on the shape of the grains. It is shown that this is a particular form of jamming that is directional in nature, since unjamming occurs if the shear direction is reversed.

A higher-order plate theory for the analysis of vibrations of thick orthotropic laminates

In this contribution, flexural vibrations of linear elastic laminates composed of thick orthotropic layers, such as cross-laminated timber, are addressed. For efficient computation, an equivalent single-layer plate theory with eight kinematic degrees of freedom is derived, both in terms of equations of motion at the continuum level and in terms of a finite element representation. The validity of the plate theory is demonstrated by comparing natural frequencies of a simply supported plate over a wide frequency range for which an analytical solution is available. Furthermore, the influence of individual material properties on the accuracy of the plate theory is investigated, demonstrating its broad applicability. The influence of material orientation on the accuracy of the plate theory is examined by comparative finite element simulations. It is shown that, for cross-ply laminates, the plate theory is valid for elements oriented at any angle to the material principal axes.

Chiral Cosserat homogenized constitutive models of architected media based on micromorphic homogenization

The present contribution aims to build chiral Cosserat effective models of architectured media prone to such effects, recoursing to dedicated homogenization methods. In order to develop a method in full generality, the effective Cosserat model is obtained from the degeneration of the micromorphic effective continuum, by projecting the micromorphic kinematic degrees of freedom onto the Cosserat variables. The proposed homogenization method relies on variational principles and a decomposition of the microscopic displacement into a so-called homogeneous part and a periodic fluctuation. The homogeneous contribution to the total microscopic displacement accounts for the postulated effective generalized continuum, and it is corrected by a displacement fluctuation. The energy of the fluctuating displacement is shown to define a measure of the accuracy of the homogenized chiral Cosserat model. Applications of the proposed homogenization framework are done for centrosymmetric and non-centrosymmetric chiral architected media.

Estimation of Joint Moments During Turning Maneuvers in Alpine Skiing Using a Three Dimensional Musculoskeletal Skier Model and a Forward Dynamics Optimization Framework.

In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.

Algorithmic design of origami mechanisms and tessellations

Origami, the ancient art of paper folding, embodies techniques for transforming a flat sheet of paper into shapes of arbitrary complexity. Although this makes origami a conceptually attractive source of inspiration when designing foldable structures and reconfigurable metamaterials for multiple functionalities, their designs are still based on a set of well-studied patterns leaving the full potential of origami inaccessible for design practitioners and researchers. Here, we present a generalized approach for the algorithmic design of rigidly-foldable origami structures exhibiting a single kinematic degree of freedom. We build on generalized conditions for rigid foldability of degree-n vertices to design origami patterns of arbitrary size and complexity. The versatility of the approach is demonstrated by its capability to not only generate, analyze and optimize regular origami patterns, but also generate and analyze kirigami, generic three-dimensional panel-hinge assemblages and their tessellations. Due to its versatility, the approach provides an inexhaustible source of foldable patterns to inspire the design of metamaterials for a wide range of applications.

Particle and Continuum Rotations of Granular Materials: Discrete-Element Method Simulations and Experiment

AbstractFor granular materials, the kinematic degrees of freedom at the microscale of particles are the particles’ displacements and rotations. In classical continuum mechanics, the kinematic degre...

Using GAMA to probe the impact of small-scale galaxy physics on nonlinear redshift-space distortions

ABSTRACT We present improved modelling of the redshift-space distortions (RSDs) of galaxy clustering that arise from peculiar velocities. We create mock galaxy catalogues in the framework of the halo model, using data from the Bolshoi project. These mock galaxy populations are inserted into the haloes with additional degrees of freedom that govern spatial and kinematical biases of the galaxy populations relative to the dark matter. We explore this generalized halo model with an Markov Chain Monte Carlo (MCMC) algorithm, comparing the predictions to data from the Galaxy And Mass Assembly survey, and thus derive one of the first constraints on the detailed kinematic degrees of freedom for satellite galaxies within haloes. With this approach, the distortions of the redshift-space galaxy autocorrelations can be accounted for down to spatial separations close to 10 kpc, opening the prospect of improved RSD measurements of the perturbation growth rate by the inclusion of data from nonlinear scales.

Higher-order Vlasov torsion theory for thin-walled box beams

Non-negligible sectional deformations, such as warping and distortion, occur in thin-walled beams under a twisting moment. For accurate analysis, these deformations need to be considered as additional kinematic degrees besides the degrees of freedom used in the classical St. Venant torsion theory. Vlasov pioneered to develop a higher-order beam theory for torsion that incorporates warping and distortion, but more sectional deformation modes than those considered in the Vlasov theory are needed to improve solution accuracy. Several theories were developed towards this direction, but no higher-order beam theory for torsion appears to allow explicit F-U and σ-F relations (U: kinematic variables, F: generalized forces, σ: stresses) as established by the Vlasov theory. In that the explicit relations are useful to interpret the physical significance of the generalized forces and can be critical in deriving explicit equilibrium conditions among the generalized forces at a joint of multiple thin-walled beams, a theory allowing the explicit relations needs to be developed. In this study, we newly propose a higher-order Vlasov torsion theory that not only includes as many torsion-related modes as desired but also provides the explicit F-U and σ-F relations that are fully consistent with those by the Vlasov theory. Towards this direction, we show that expressing the σ-U relation only with sectional mode shapes orthogonal to each other is critical in establishing explicit F-U and σ-F relations. We then establish new recursive relations that can be used to express each of derivatives for the sectional mode shapes involved in the σ-U relation as a linear combination of other orthogonal sectional mode shapes. In the developed theory, even stresses at off-centerline positions of the beam cross-section are explicitly related to F. The validity and accuracy of the proposed theory are confirmed by examining displacements, stresses, and eigenfrequencies for several torsion problems. The numerical results by the proposed theory are in good agreement with those by the shell analysis.

The effect of patellofemoral pain syndrome on patellofemoral joint kinematics under upright weight-bearing conditions.

Patellofemoral pain (PFP) is commonly caused by abnormal pressure on the knee due to excessive load while standing, squatting, or going up or down stairs. To better understand the pathophysiology of PFP, we conducted a noninvasive patellar tracking study using a C-arm computed tomography (CT) scanner to assess the non-weight-bearing condition at 0° knee flexion (NWB0°) in supine, weight-bearing at 0° (WB0°) when upright, and at 30° (WB30°) in a squat. Three-dimensional (3D) CT images were obtained from patients with PFP (12 women, 6 men; mean age, 31 ± 9 years; mean weight, 68 ± 9 kg) and control subjects (8 women, 10 men; mean age, 39 ± 15 years; mean weight, 71 ± 13 kg). Six 3D-landmarks on the patella and femur were used to establish a joint coordinate system (JCS) and kinematic degrees of freedom (DoF) values on the JCS were obtained: patellar tilt (PT, °), patellar flexion (PF, °), patellar rotation (PR, °), patellar lateral-medial shift (PTx, mm), patellar proximal-distal shift (PTy, mm), and patellar anterior-posterior shift (PTz, mm). Tests for statistical significance (p < 0.05) showed that the PF during WB30°, the PTy during NWB0°, and the PTz during NWB0°, WB0°, and WB30° showed clear differences between the patients with PFP and healthy controls. In particular, the PF during WB30° (17.62°, extension) and the PTz during WB0° (72.5‬0 mm, posterior) had the largest rotational and translational differences (JCS Δ = patients with PFP—controls), respectively. The JCS coordinates with statistically significant difference can serve as key biomarkers of patellar motion when evaluating a patient suspected of having PFP. The proposed method could reveal diagnostic biomarkers for accurately identifying PFP patients and be an effective addition to clinical diagnosis before surgery and to help plan rehabilitation strategies.

Refined Zigzag Theory: an appropriate tool for the analysis of CLT-plates and other shear-elastic timber structures

Cross laminated timber (CLT), as a structural plate-like timber product, has been established as a load bearing product for walls, floor and roof elements. In a bending situation due to the transverse shear flexibility of the crossing layers, the warping of the cross section follows a zigzag pattern which should be considered in the calculation model. The Refined Zigzag Theory (RZT) can fulfill this requirement in a very simple and efficient way. The RZT, founded in 2007 by A. Tessler (NASA Langley Research Center), M. Di Sciuva and M. Gherlone (Politecnico Torino) is a very robust and accurate analysis tool, which can handle the typical zigag warping of the cross section by introducing only one additional kinematic degree of freedom in case of plane beams and two more in case of biaxial bending of plates. Thus, the RZT-kinematics is able to reflect the specific and local stress behaviour near concentrated loads in combination with a warping constraint, while most other theories do not. A comparison is made with different methods of calculation, as the modified Gamma-method, the Shear Analogy method (SA) and the First Order Shear Deformation Theory (FSDT). For a test example of a two-span continuous beam, an error estimation concerning the maximum bending stress is presented depending on the slenderness L/h and the width of contact area at the intermediate support. A stability investigation shows that FSDT provides sufficiently accurate results if the ratio of bending and shear stiffness is in a range as stated in the test example. It is shown that by a simple modification in the determination of the zigzag function, the scope can be extended to beams with arbitrary non-rectangular cross section. This generalization step considerably improves the possibilities for the application of RZT. Furthermore, beam structures with interlayer slip can easily be treated. So the RZT is very well suited to analyze all kinds, of shear-elastic structural element like CLT-plate, timber-concrete composite structure or doweled beam in an accurate and unified way.

Biomechanics of Cervical Disc Arthroplasty-A Review of Concepts and Current Technology.

Activities of daily living require the subaxial cervical spine (C2-C7) to have substantial mobility. Cervical degenerative changes can cause abnormal motions and altered load distribution, leading to pain and limiting the ability of individuals to perform activities of daily living. Anterior cervical discectomy and fusion (ACDF) has been widely used to treat symptomatic cervical spondylosis. Clinical studies have shown cervical disc arthroplasty (CDA) to be a viable alternative to ACDF for the treatment of radiculopathy and myelopathy. The benefits of CDA are based on the premise that preservation of physiologic motions and load-sharing at the treated level would lead to longevity of the index-level facet joints and mitigate the risk of adjacent segment degeneration.This review article classifies cervical disc prostheses according to their kinematic degrees of freedom and device constraints. Discussion on how these design features may affect cervical motion after implantation will provide the reader with valuable information on how disc prostheses may function clinically.The ability of a disc prosthesis to work in concert with remaining bony and soft tissue structures to restore physiologic motion and load-sharing is a function of the following design features and surgical factors: Kinematic degrees of freedom-Prostheses that allow translation independent of rotation allow, in theory, the spinal anatomy to dictate segmental motion after CDA potentially restoring physiologic motion and load-sharing. A 6-degrees-of-freedom disc prosthesis may be best equipped to achieve the intended function of CDA.Built-in stiffness-A disc prosthesis with built-in resistance to angular and translational motion may have an advantage in restoring stability to a hypermobile segment without eliminating motion.Surgical factors related to prosthesis implantation may influence cervical segments after CDA. These factors include the amount of disc space distraction caused by the prosthesis, prosthesis placement in the sagittal and coronal planes, and integrity of the soft tissue envelope.

Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body

Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.