Minimal Degrees Of Freedom Research Articles

Snap-through and indirect reduced-order modelling

Snap-through is a nonlinear jump phenomenon that is increasingly being designed into engineering structures. The rich and varied dynamics of snap-through present a significant bottleneck in the design process as costly dynamic simulations are required to ensure predictable behaviour. The purpose of this research is to investigate the use of a recent projection-based, reduced-order modelling technique, namely, implicit condensation and expansion with inertial compensation, to reproduce the snap-through behaviours found in bistable finite element systems in analogous models with minimal degrees of freedom. In this work, the free response of a simple mass-spring oscillator is used to differentiate different types of snap-through. This provides a framework for discussing the dynamics of a family of buckled beams. The ability of the reduced-order models to faithfully reproduce these dynamics is investigated by testing the existence and stability of predicted periodic orbits. It is shown that the minimum projection basis required to capture snap-through accurately can be found through considering the minimum energy required for different types of snap-through. For bistable beams, this can be further simplified to just requiring an eigenvalue analysis at the most unstable equilibrium.

Natural metric-affine inflation

We consider here natural inflation in the low energy (two-derivative) metric-affine theory containing only the minimal degrees of freedom in the inflationary sector, i.e. the massless graviton and the pseudo-Nambu-Goldstone boson (PNGB). This theory contains the Ricci-like and parity-odd Holst invariants together with non-minimal couplings between the PNGB and the above-mentioned invariants. The Palatini and Einstein-Cartan realizations of natural inflation are particular cases of our construction. Explicit models of this type featuring non-minimal couplings are shown to emerge from the microscopic dynamics of a QCD-like theory with an either sub-Planckian or trans-Planckian confining scale and that is renormalizable on Minkowski spacetime. Moreover, for these models, we find regions of the parameter space where the inflationary predictions agree with the most recent observations at the 2σ level. We find that in order to enter the 1σ region it is necessary (and sufficient) to have a finite value of the Barbero-Immirzi parameter and a sizable non-minimal coupling between the inflaton and the Holst invariant (with sign opposite to the Barbero-Immirzi parameter). Indeed, in this case the potential of the canonically normalized inflaton develops a plateau as shown analytically.

Soft-landing dynamics of a type of four-legged space lander

Analyzing the landing dynamics response is essential for enhancing the success rate of surface explorations on celestial bodies like Mars, the moon, and asteroids. This paper develops a comprehensive dynamics model for a space lander equipped with four sets of buffer legs. Each set comprises a primary strut, two secondary struts, and a footpad. The compression force of the buffer struts is determined through interpolation of real experimental data, while the contact force between the footpad and the ground is calculated using Archimedes law for granular media. The Lagrange equation of the second kind is employed to construct the dynamical model for the lander with minimal degrees of freedom. The proposed dynamics model is validated through experiments involving touchdowns of a single legged lander and a four legged lander. Moreover, key physical quantities such as the buffer force, energy absorption and body acceleration are computed for both 1-2-1 and 2-2 landing configurations. The results indicate that the buffer strut is capable of absorbing approximately half of the impact energy, leading to a 50-fold reduction in the shock acceleration of the main body in both landing configurations. However, it is observed that the maximum compression of the buffer strut is greater in the 1-2-1 landing configuration than in the 2-2 landing configuration. Furthermore, these simulations can be completed within seconds, enabling extensive simulations for the design and optimization of soft landing processes.

Robotic system for nasopharyngeal swab sampling based on remote center of motion mechanism.

In this study, a robotic system is proposed for nasopharyngeal (NP) swab sampling with high safety and efficiency. Most existing swab-sampling robots have more than six degrees of freedom (DOFs). However, not all six DOFs are necessarily required for NP swab sampling. A high number of DOFs can cause safety problems, such as collisions between the robot and patient. We developed a new type of robot with four DOFs for NP swab sampling that consists of a two DOFs remote center of motion (RCM) mechanism, a two DOFs insertion mechanism, and a nostril support unit. With the nostril support unit, the robot no longer needs to adjust the insertion position of the swab. The proposed robot enables the insertion orientation and depth to be adjusted according to different postures or facial shapes of the subject. For intuitive and precise remote control of the robot, a dedicated master device for the RCM and a visual feedback system were developed. The effectiveness of the robotic system was demonstrated by repeatability, RCM accuracy, tracking accuracy, and in vitro phantom experiments. The average tracking error between the master device and the robot was less than 2mm. The contact force exerted on the swab prior to reaching the nasopharynx was less than 0.04 N, irrespective of the phantom's pose. This study confirmed that the RCM-based robotic system is effective and safe for NP swab sampling while using minimal DOFs.

Increased signal-to-noise ratios within experimental field trials by regressing spatially distributed soil properties as principal components.

Environmental variability poses a major challenge to any field study. Researchers attempt to mitigate this challenge through replication. Thus, the ability to detect experimental signals is determined by the degree of replication and the amount of environmental variation, noise, within the experimental system. A major source of noise in field studies comes from the natural heterogeneity of soil properties which create microtreatments throughout the field. In addition, the variation within different soil properties is often nonrandomly distributed across a field. We explore this challenge through a sorghum field trial dataset with accompanying plant, microbiome, and soil property data. Diverse sorghum genotypes and two watering regimes were applied in a split-plot design. We describe a process of identifying, estimating, and controlling for the effects of spatially distributed soil properties on plant traits and microbial communities using minimal degrees of freedom. Importantly, this process provides a method with which sources of environmental variation in field data can be identified and adjusted, improving our ability to resolve effects of interest and to quantify subtle phenotypes.

Finite-Volume Method Enables Simulation of Induced Seismicity

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203903, “A Collocated Finite-Volume Scheme for High-Performance Simulation of Induced Seismicity in Geoenergy Applications,” by A. Novikov, D.V. Voskov, SPE, and M. Khait, SPE, Delft University of Technology, et al. The paper has not been peer reviewed. In the complete paper, the authors develop a collocated finite-volume method (FVM) to study induced seismicity as a result of pore-pressure fluctuations. A discrete system is obtained based on a fully implicit coupled description of flow, elastic deformation, and contact mechanics at fault surfaces on a fully unstructured mesh. The cell-centered collocated scheme leads to convenient integration of the different physical equations because the unknowns share the same discrete locations on the mesh. Additionally, a multipoint flux approximation is formulated in a general procedure to treat heterogeneity, anisotropy, and cross-derivative terms for both flow and mechanics equations. Introduction The FVM has become an essential tool for flow and transport simulation because of its local conservation property. For mechanical deformation, however, the conservation property does not have the same importance. Nonetheless, the FVM is still an attractive choice because it represents conservation laws in integral form more naturally. Some authors in the literature use fixed-stress splitting algorithms to decouple mechanics and flow equations. These are a form of sequential implicit solution schemes and often lead to more-efficient simulations than fully implicit (FI) simulation. However, sequential schemes introduce certain restrictions on timestep sizes. On the other hand, FI schemes provide unconditionally convergent solutions and are more-robust and -convenient approaches for investigation of complex multiphysical problems. Although the FI approach does not imply any restriction on timestep size, it requires an efficient linear equation solution strategy for high-resolution models. In this study, the authors develop a collocated FI multipoint FVM scheme for poromechanics simulation of faulted reservoirs. The scheme can be used to solve poromechanics problems on unstructured polyhedral grids with minimal degrees of freedom per cell. It is also capable of considering material heterogeneity while preserving mass and momentum balances. This scheme is extended to consider discontinuities in displacements at faults. The developed algorithms have been embedded into the open-source Delft Advanced Research Terra Simulator (DARTS).

Minimal supergravity inflation without slow gravitino

We utilize a recently proposed cubic nilpotent superfield to realize inflation in supergravity with the minimal degrees of freedom: the inflaton, graviton, and massive gravitino. As an advantage, the resultant model is free from the catastrophic production of gravitinos due to its vanishing propagation speed. However, the model suffers from the standard gravitino problem, and its viability depends on the mass spectrum and the thermal history of the universe.

Generic “unnecessary” quantum critical points with minimal degrees of freedom

We explore generic "unnecessary" quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions. In this work we seek for examples of generic unnecessary quantum critical points with minimal degrees of freedom. In particular, in three dimensional space, we identify two examples of such generic unnecessary quantum critical points. The first example occurs in a $3d$ interacting topological insulator, and it is described by $two$ $(3+1)d$ massless Dirac fermions in the infrared limit; the second example occurs in a $3d$ topological superconductor, and it is formally described only $one$ $(3+1)d$ massless Dirac fermion.

Axion structure formation – I: the co-motion picture

Axions as dark matter is an increasingly important subject in astrophysics and cosmology. Experimental and observational searches are mounting across the mass spectrum of axion-like particles, many of which require detailed knowledge of axion structure over a wide range of scales. Current understanding of axion structures is far from complete, however, due largely to controversy in modeling the candidate's highly-degenerate state. The series Axion Structure Formation seeks to develop a consistent model of QCD axion dark matter dynamics that follows their highly-degenerate nature to the present using novel modeling techniques and sophisticated simulations. This inaugural paper presents the problem of describing many non-relativistic axions with minimal degrees of freedom and constructs a theory of axion infall for the limit of complete condensation. The derived model is shown to contain axion-specific dynamics not unlike the exchange-correlation influences experienced by identical fermions. Perturbative calculations are performed to explore the potential for imprints in early universe structures.

Simple left-right theory: Lepton number violation at the LHC

We propose a simple left-right symmetric theory where the neutrino masses are generated at the quantum level. In this context the neutrinos are Majorana fermions and the model has the minimal degrees of freedom in the scalar sector needed for symmetry breaking and mass generation. We discuss the lepton number violating signatures with two charged leptons of different flavor and missing energy at the Large Hadron Collider in order to understand the testability of the theory.

Immersed Boundary Simulations of Active Fluid Droplets.

We present numerical simulations of active fluid droplets immersed in an external fluid in 2-dimensions using an Immersed Boundary method to simulate the fluid droplet interface as a Lagrangian mesh. We present results from two example systems, firstly an active isotropic fluid boundary consisting of particles that can bind and unbind from the interface and generate surface tension gradients through active contractility. Secondly, a droplet filled with an active polar fluid with homeotropic anchoring at the droplet interface. These two systems demonstrate spontaneous symmetry breaking and steady state dynamics resembling cell motility and division and show complex feedback mechanisms with minimal degrees of freedom. The simulations outlined here will be useful for quantifying the wide range of dynamics observable in these active systems and modelling the effects of confinement in a consistent and adaptable way.

動作自由度数を低減した脚車輪型移動ロボットの駆動機構と歩行および走行の双方向切り換え制御

This paper proposes a design concept for renovating a legged robot to a hybrid mobile robot with minimal degrees of freedom (4DOFs) and its motion analysis for switching locomotion from leg-type to wheel-type and vice versa. For the leg-type locomotion, specifically in the transitional state of sitting or standing, we show the control method based on minimization of total energy cost considering the distribution of a motor power payload in hip and knee joints using a motor specification. Also, we discuss robot configurations for switching between the two types under such environmental factors like walking gaits, ground inclination angle and traveling direction. Knee joint position of a pivotal foot determines knee ahead and knee behind gaits. Then we find three beneficial switching types aiming for moderate use of motor, rider's comfort, and energy saving. Moreover, we clarify the control method for changing traveling direction within a switching period. Finally, we demonstrate the switching and verify that the results of the analysis become useful for enabling the switch on demand. Also, the demonstration verifies that the robot can generate a steering function while it switches between the two types of locomotion.

Higher order zig-zag theory for smart composite shells under mechanical-thermo-electric loading

A higher order zig-zag shell theory based on general tensor formulation is developed to refine the predictions of the mechanical, thermal, and electric behaviors. All the complicated curvatures of surface including twisting curvatures can be described in a geometrically exact manner in the present shell theory because the present theory is based on the geometrically exact surface representation. The in-surface displacement fields are constructed by superimposing the linear zig-zag field to the smooth globally cubic varying field through the thickness. Smooth parabolic distribution through the thickness is assumed in the out-of-plane displacement in order to consider transverse normal deformation and stress. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface free conditions of transverse shear stresses. Thus the proposed theory has only seven primary displacement unknowns and they do not depend upon the number of layers. To assess the validity of present theory, the developed theory is evaluated under the thermal and electric load as well as under the mechanical load of composite cylindrical shells. Through the numerical examples, it is demonstrated that the proposed smart shell theory is efficient because it has the minimal degrees of freedom. The present theory is suitable in the predictions of deformation and stresses of thick smart composite shells under the mechanical, thermal, and electric loads combined.

Residual-effected homogeneous charge compression ignition with delayed intake-valve closing at elevated compression ratio

Residual-effected homogeneous charge compression ignition (HCCI) was investigated using a single-cylinder research engine equipped with fully-flexible variable valve actuation. Operation at elevated compression ratios was explored to determine its effect on efficiency. Results showed that efficiency is decreased significantly by advanced phasing owing to increased thermal losses. However, if combustion phasing is held fixed, elevated compression ratio operation showed little effect on efficiency. Further experiments explored the use of IVC time as a control parameter at the elevated compression ratio. Tests were conducted to determine if an efficiency benefit could be realized from increasing the compression ratio and delaying IVC to increase the extent of expansion relative to compression. No significant change in efficiency was observed, although variation in IVC timing offered significant control authority. Delayed IVC was used in conjunction with variable IVO to control independently load and phasing of HCCI at the elevated compression ratio. Tests were also conducted to assess the significance of the measured exhaust temperature on HCCI phasing. EVO was introduced as a third control parameter, along with IVO and IVC, to control independently initial mixture composition, compression work, and exhaust temperature. Results indicated that the measured exhaust temperature was not a good indicator of HCCI phasing and suggested the stabilizing role of heat transfer to the reinducted exhaust gases. Results also suggested a set of control parameters that achieve the full range of HCCI operation with minimal degrees of freedom.

Reproducing kernel element method Part III: Generalized enrichment and applications

In this part of the work, a notion of generalized enrichment is proposed to construct the global partition polynomials or to enrich global partition polynomial basis with extra terms corresponding to the higher order derivatives of primary variable. This is accomplished by either multiplying enrichment functions with the original global partition polynomials, or increasing the order of global partition polynomials in the same mesh. Without refining mesh, high order consistency in interpolation hierarchy with generalized Kronecker delta property can be straightforwardly achieved in quadrilateral and triangular mesh in 2D by the proposed scheme. Comparing with the traditional finite element methods, the construction proposed here has more flexibility and only needs minimal degrees of freedom. The optimal element with high reproducing capacity and overall minimal degrees of freedom can be constructed by the generalized enrichment procedure. Two optimal elements in two dimensional space have been constructed: T10P3I 4 3 triangular element satisfies third order consistency condition with only 10 degrees of freedom, and Q15P4I 4 3 quadrilateral element satisfies fourth order consistency condition with 15 degrees of freedom. The performance of interpolation hierarchy is evaluated through solving some bench-mark problems for thin (Kirchhoff) plates.

Reproducing kernel element method Part II: Globally conforming Im/ Cn hierarchies

In this part of the work, a minimal degrees of freedom, arbitrary smooth, globally compatible, I m / C n interpolation hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary multiple dimensional domains. This is the first interpolation hierarchical structure that has been constructed with both minimal degrees of freedom and higher order smoothness or continuity over multi-dimensional domain. The proposed hierarchical structure possesses the generalized Kronecker property, i.e. ∂ αΨ (β) I/ ∂x α(x J)=δ IJδ αβ, |α|,|β|⩽m. This contribution is the latest breakthrough of an outstanding problem––construction of a minimal degrees of freedom, globally conforming, I m / C n finite element interpolation fields on an arbitrary mesh or subdivision of multiple dimension. The newly constructed globally conforming interpolant is a hybrid of a set of C ∞ global partition polynomials with a highly smooth ( C n ) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.

Reproducing kernel element method. Part IV: Globally compatible [formula omitted] triangular hierarchy

In this part of the work, a globally compatible C n(Ω) triangular element hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary two dimensional domains. In principle, the smoothness of the globally conforming element can be made arbitrarily high ( n⩾1). The triangle interpolation field can interpolate the derivatives of an unknown function up to arbitrary mth order, ( I m ), and it can reproduce complete kth order polynomials with k⩾ m. This is the first interpolation hierarchical structure that has ever been constructed with both minimal degrees of freedom and higher order smoothness and continuity over discretizations of a multiple dimensional domain. The performance of the newly constructed compatible element is evaluated in solving several Kirchhoff plate problems.

The Grammar of Action: "Phrase Structure" in Children's Copying

NINIO, ANAT, and LIEBLICH, AMIA. The Grammar of Action: Phrase Structure in Children's Copying. CHILD DEVELOPMENT, 1976, 47, 846-849. 30 4-5-year-old children copied a horizontal line, a vertical line, and an inverted T. Preference for a certain strategy in copying the compound figure was interpreted in terms of a simple phrase structure, one involving movements controlled with minimal degrees of freedom. Considerations of the total utterance in terms of semantics and phrase structure are necessary to account for copying patterns. In a second experiment, 163 children from kindergarten through sixth grade were given the inverted-T copying task. With increased age, children come to prefer increasingly complex combinational structures.