Phase Stiffness Research Articles

From a biological template model to gait assistance with an exosuit

The invention of soft wearable assistive devices, known as exosuits, introduced a new aspect in assisting unimpaired subjects. In this study, we designed and developed an exosuit with compliant biarticular thigh actuators called BATEX. Unlike the conventional method of using rigid actuators in exosuits, the BATEX is made of serial elastic actuators (SEA) resembling artificial muscles. This bioinspired design is complemented by the novel control concept of using the ground reaction force to adjust the artificial muscles’ stiffness in the stance phase. By locking the motors in the swing phase, the SEAs will be simplified to passive biarticular springs, which is sufficient for leg swinging. The key concept in our design and control approach is to synthesize human locomotion to develop an assistive device instead of copying human motor control outputs. Analyzing human walking assistance using experiment-based OpenSim simulations demonstrates the advantages of the proposed design and control of BATEX, such as 9.4% reduction in metabolic cost during normal walking condition. This metabolic reduction increases to 10.4% when the subjects carry a 38 kg load. The adaptability of our proposed model-based control to such an unknown condition outperforms the assistance level of the model-free optimal controller. Moreover, increasing the assistive system’s efficiency by adjusting the actuator compliance with the force feedback supports our previous findings on the LOPES II exoskeleton.

Comparison of anterior knee laxity, stiffness, genu recurvatum, and general joint laxity in the late follicular phase and the ovulatory phase of the menstrual cycle

BackgroundOne risk factor for anterior cruciate ligament (ACL) injury may be fluctuations in female hormones. This study examined variability in joint laxity, as a risk factor for ACL injury, during the menstrual cycle.MethodsSubjects were 15 female university students with regular menstrual cycles. We measured estradiol (E2) concentration, anterior knee laxity (AKL), stiffness, genu recurvatum (GR), and general joint laxity (GJL) during the late follicular and ovulatory phases. AKL was measured as anterior tibial displacement of the femur after application of 44-, 89-, and 133-N loads on the tibia. Stiffness was calculated as Δforce/Δdisplacement at loads of 44–89 N and between 89 and 133 N. GR was measured prone, with the base of the patella distal to the edge of the bed. The University of Tokyo joint laxity test was used to evaluate GJL.ResultsE2 concentration was significantly higher in the ovulatory phase than in the late follicular phase (p = 0.018), AKL and stiffness did not differ significantly between phases, and GR and GJL were significantly higher in the ovulatory phase than in the late follicular phase (p = 0.011, 0.031).ConclusionThese findings suggest that E2 concentrations may affect GR and GJL during the menstrual cycle.

Competing phases and critical behaviour in three coupled spinless Luttinger liquids

We study electronic phase competition in a strongly correlated system of three coupled spinless Luttinger liquids—one of the simplest models where topologically nontrivial chiral orders may be realized. We study the problem as a coupled sine-Gordon model, using a perturbative renormalization group (RG) approach. In contrast with counterparts with fewer fermionic species, here the scaling procedure generates off-diagonal contributions to the phase stiffness matrix, which require both rescaling as well as large rotations of the bosonic fields. These rotations, generally non-abelian in nature, introduce a coupling between different interaction channels even at the tree-level order in the coupling constant scaling equations. We study competing phases in this system, taking into account the aforementioned rotations, and determine its critical behaviour in a variety of interaction parameter regimes where perturbative RG is possible. The phase boundaries are found to be of the Berezinskii–Kosterlitz–Thouless type, and we specify the parameter regimes where symmetry breaking between the three flavours of bosonic fields, orders involving different flavours, and chiral orders may be observed. Our approach and findings may be relevant for understanding phases and transitions at high magnetic fields in semimetals such as bismuth featuring three Fermi pockets.

Does filling-dependent band renormalization aid pairing in twisted bilayer graphene?

Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.

Fixed Points on Active and Passive Dynamics of Active Hydraulic Mounts with Oscillating Coil Actuator

Active hydraulic mounts with an inertia track, decoupler membrane, and oscillating coil actuator (AHM-IT-DM-OCAs) have been studied extensively due their compact structure and large damping in the low-frequency band. This paper focuses on a comprehensive analysis of the active and passive dynamics and their fixed points in mid-low-frequency bands, which will be helpful for parameter identification. A unified lumped parameter mechanical model with two degrees-of-freedom is established. The inertia and damping forces of the decoupler/actuator mover may be neglected, and a nonlinear mathematical model can be obtained for mid-low-frequency bands. Theoretical analysis of active and passive dynamics for fluid-filled state reveals the amplitude dependence and a fixed point in passive dynamic stiffness in-phase or active real-frequency characteristics. The amplitude dependence of local loss at the fluid channel entrance and outlet induces the amplitude-dependent dynamics. The amplitude-dependent dynamics constitute a precondition for fixed points. A single fixed point in passive dynamics is experimentally validated, and a pair of fixed points in active dynamics for an AHM-IT-DM-OCA is newly revealed in an experiment, which presents a new issue for further analysis.

Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.

Nonlinear wave in granular systems based on elastoplastic dashpot model

AbstractThe dynamic dashpot models are widely used in EDEM commercial software. However, most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact velocity. Moreover, the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact phase. These two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular chain. Therefore, this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular matters. First, the entire contact process is divided into three different phases: elastic, elastoplastic, and full plastic phases. The Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic phase. Hertz contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma‐Liu (ML) model in each time step. Second, the whole contact behavior is treated as a linear mass‐spring‐damper model, and the damping factor is obtained by solving the single‐degree‐freedom underdamped vibration equation. The new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors, which not only removes the initial impact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic phase. Finally, a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental data. The simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.

Stimuli‐responsive hydrogels: Fabrication and biomedical applications

AbstractDue to their similarity to some bio‐architectures, for example, extracellular matrix, hydrogels are considered as bio‐inspired networks with bio‐mimetic and bio‐functional properties. With natural cytocompatibility and biocompatibility, hydrogels nowadays are more and more involved in various bio‐applications including shape morphing, artificial muscles, soft robotics, regenerative medicine, and so on. As an important subclass, stimuli‐responsive hydrogels have been attracting interest within decades. In response to single or multi‐triggers in biological microenvironment, stimuli‐responsive hydrogels can undergo phase transition, stiffness change, or biochemical properties activation, which make them intriguing biomaterials with broad applications including sensing, drug delivery, tissue engineering, and wound healing. This review presents typical synthetic and natural gelators comprising small molecules and polymers as building blocks of functional architectures. The fabrication strategies of hydrogels varied from supramolecular assembly to dynamic covalent binding are detailed. Various exogenous or endogenous, physical or chemical, and synthetic or natural stimuli together with response mechanism, design principle are demonstrated. Through recent examples from different perspectives, such as bionic devices, wound dressing, and cargo carrier, the benefits and opportunities of stimuli‐responsive hydrogels for biological applications are highlighted. Finally, the current challenges and future prospects in view of translation from fundamental researches to clinical application are briefly discussed.

Optical spectral weight, phase stiffness, and Tc bounds for trivial and topological flat band superconductors

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D) [Formula: see text] We focus on on-site attraction [Formula: see text] on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight [Formula: see text] with [Formula: see text] , where n is the flat-band density and Ω is the Marzari-Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for [Formula: see text] linear in [Formula: see text] We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

Evaluation of Linear Deformation and Unloading Stiffness Characteristics of Asphalt Mixtures Incorporating Various Aggregate Gradations

Optimum stiffness and linear deformation in the unloading phase are fundamental properties of asphalt mixtures required for the durability of flexible pavements. In this research, blends of six different aggregate gradations were used for two base course (BC) and four wearing course (WC) asphalt mixtures. Stability and indirect tensile strength of resulting asphalt mixtures were evaluated to relate to viscoelastic unloading deformation and resilient moduli (instantaneous (MRI) and total (MRT)) at 25 °C using a 40/50 binder for 0.1 and 0.3 s load durations. Results indicated that an increase in coarse aggregate proportion from 48 to 70% for BC has shown a 12% and 14% increase in MRT for 0.1 and 0.3 s load durations, respectively, and an increase in coarse aggregate proportion from 41 to 57.5% for WC has caused a 26% and 20% increase in MRI for 0.1 and 0.3 s load durations, respectively. The same coarse aggregate proportions showed an increase in linear viscoelastic deformation at 0.1 s load duration from 54.6 to 68.2% for WC and from 53.0 to 62.7% for BC, whereas for 0.3 s load duration linear viscoelastic deformation increased from 58.1 to 69.1% for WC and 64.3 to 69.2% for BC. The findings of this study will assist in the selection of aggregate gradations to be used in wearing and base course asphalt mixtures for pavement design, construction and maintenance.

Strain-induced structural phase transition in GeN monolayer

The recent synthesis of SiP, SiAs, GeP, and GeAs monolayers has brought two-dimensional (2D) group IV–V systems into the limelight. To date, all the fabricated structures of this class belong to the C2/m space group which has a low structural symmetry, while the class could exist in more symmetric phases (i.e., P3¯m1 and P6¯m2). The realization of more symmetric phases can enhance the intrinsic properties of these materials and increase their potential field of usage. In this study, the possibility of a structural phase transition in GeN monolayer by application of mechanical strain is investigated. Based on ab initio simulations, we first confirm the stability of the GeN monolayer in all phases, then demonstrate how a large enough compressive strain (∼12%) can transform C2/m into P3¯m1 phase. The results are interpreted by analyzing the geometry, bond order, electron localization functions, and net atomic charges of the structures. Upon transition into the P3¯m1 phase, tensile strength and in-plane stiffness double, while the compressive strength quadruples. On the other hand, the effect of the phase transition on the electronic properties is not substantial and similar band structure profiles with narrowed band gap are obtained. Our study provides insight on how to experimentally achieve the P3¯m1 phase of the GeN monolayer, which is in principle applicable to other group IV–V monolayers under suitable conditions involving the optimization of pressure, temperature, and impurity concentration. These unique features of the GeN monolayer render them ideal candidates for a variety of high technological nanoscale applications.

Effects of Tendon Release Surgery on Inter-Limb Leg Stiffness Control in Children with Spastic Diplegic Cerebral Palsy during Gait

Impaired motor control and musculotendon tightness in the lower extremities are characteristic features of patients with diplegic cerebral palsy (CP). Tendon release surgery (TRS) helps improve joint and leg stiffness, but the effects of TRS on inter-limb coordination in terms of the total leg stiffness, and the bilateral symmetry in leg stiffness during gait, remain unknown. Ten children with spastic diplegic CP scheduled for TRS and ten healthy controls participated in this study. The inter-limb sharing of total leg stiffness during double-limb support phase and bilateral leg stiffness symmetry during stance phase of gait were calculated using the kinematic and ground reaction force data measured by a motion analysis system. Before TRS, the patients with diplegic CP walked with a decreased share of total leg stiffness during weight-acceptance (p < 0.05) and with increased bilateral leg stiffness asymmetry during single-limb support and weight-transfer during gait (p < 0.05) when compared to healthy controls. After TRS, the bilateral leg stiffness asymmetry was significantly reduced in the CP group, especially in the terminal stance phase, with inter-limb sharing of total leg stiffness becoming similar to that in controls (p > 0.05). The surgery seemed to improve the lower limb control and increased the bilateral limb symmetry during gait.

Some Aspects of Shear Behavior of Soft Soil-Concrete Interfaces and Its Consequences in Pile Shaft Friction Modeling.

This paper examines the stiffness degradation and interface failure load on soft soil–concrete interface. The friction behavior and its variability is investigated. The direct shear tests under constant normal load were used to establish parameters to hyperbolic interface model which provided a good approximation of the data from instrumented piles. Four instrumented piles were used to obtain reference soil–concrete interface behavior. It was found that the variability of the friction characteristics is the highest for organic clays and the lowest for organic silts. The intact samples exhibit lower shear strength than reconstituted ones. The adhesion varies significantly depending on interface and soil type, which can result in high scatter of the skin friction prediction. The analysis of parameters variability can be used to determine the upper and lower bound of friction behavior on the interface at constant normal load condition. The backward shearing results in decrease in shear strength up to 40% of the precedent forward phase but higher initial stiffness by a factor of between 2 and 3. Presented research provides basic shear and stiffness parameters for four soft soils (organic clay, organic silt, peat, and silty loam) and gives information about variability of interface characteristics.

Reconstruction of Three-Dimensional Microstructures of Two-Phase Membrane and Phase Property Estimation Through Combination of Experiment and Simulation

In this study, a multiscale property evaluation framework for heterogeneous materials with complex microstructures on a sub-micro scale has been proposed. A detailed investigation of the three-dimensional (3D) microstructural features is necessary for the evaluation of the properties of heterogeneous materials with complex microstructures. However, for heterogeneous materials with microstructures on a sub-micro scale, it is difficult to observe the 3D microstructural features owing to the limit of resolution. In this study, virtual 3D samples were reconstructed based on two-dimensional images, and tensile simulations were performed using the reconstructed 3D samples instead of the real 3D microstructures. The input parameters for the tensile-property simulations were measured via atomic force microscopy, which is used to measure the phase stiffness on a sub-micro scale. The results from these simulations were then compared with those of the experiment on a macro scale to confirm the correlation between the mechanical properties measured on the sub-micron and macro scales.

Liver stiffness in the early post-liver transplant phase as a marker of acute allograft rejection

Introduction: Acute allograft rejection remains a relevant post-operative complication after liver transplantation. Diagnosis of acute rejection is today based on clinical, laboratory and histopathological criteria. A prompt diagnosis of rejection is crucial.

Midfoot passive stiffness affects foot and ankle kinematics and kinetics during the propulsive phase of walking

The midfoot joint complex (MFJC) is related to the mechanics and efficiency of the walking propulsive phase and low midfoot passive stiffness may require compensatory foot and ankle joint moments to avoid excessive pronation and inefficient propulsion. This study aimed to investigate the kinematics and kinetics of the MFJC and ankle during the propulsive phase of walking in subjects with larger and smaller midfoot passive stiffness. MFJC passive stiffness of 20 healthy adult participants, and the kinematics and kinetics of the MFJC (forefoot-rearfoot) and ankle (rearfoot-shank) during the stance phase of walking were measured. The participants were divided equally into two groups according to the MFJC passive stiffness. Ranges of motion (ROM) and mean joint moments were computed for the late stance. Independent t-tests (α = 0.05) revealed that subjects with lower midfoot passive stiffness showed an increased MFJC sagittal ROM (flattened longitudinal arch) (p = 0.002), increased ankle frontal ROM (more everted positions) (p = 0.002), increased MFJC frontal ROM (more inverted positions) (p = 0.019), as well as a tendency for larger ankle sagittal ROM (p = 0.056). They also showed increased MFJC (p = 0.021) and ankle (p = 0.018) moments in the sagittal plane, increased MFJC moment in the frontal plane (p = 0.047) and a tendency for a predominant ankle moment in the frontal (p = 0.058). Foot and ankle joint moments are possible strategies to reduce pronation and improve propulsion, but not sufficient to prevent the altered kinematics related to low midfoot stiffness. Therefore, midfoot passive stiffness is critical for foot and ankle kinematics and kinetics during walking propulsive phase and is a potential target of interventions.

The charge-density-wave signature on the superfluid density of cuprate superconductors

The superfluid density or superconducting (SC) carrier concentration n sc of cuprates has been the subject of intense investigations but there is not any single theory capable to explain all the available data. Here we show that the behavior of n sc in under and overdoped cuprates are a consequence of an SC interaction based on charge fluctuations in the incommensurate charge-density-waves (CDW) domains. We have shown that this interaction scales with the CDW amplitude or the pseudogap (PG) energy, yielding local SC amplitudes and Josephson currents. The average Josephson energy is proportional to the phase stiffness or superfluid density ρ sc ∝ n sc. We find that n sc(p) increases almost linearly with doping p in the underdoped region and in the charge abundant overdoped only a few fractions of the holes condense leading to two kinds of carriers, a recently confirmed feature. The calculations and the ρ sc data uncover how the PG–CDW–SC intertwined orders operate to yield cuprates properties.

Non-linear Terahertz driving of plasma waves in layered cuprates

The hallmark of superconductivity is the rigidity of the quantum-mechanical phase of electrons, responsible for superfluid behavior and Meissner effect. The strength of the phase stiffness is set by the Josephson coupling, which is strongly anisotropic in layered cuprates. So far, THz light pulses have been used to achieve non-linear control of the out-of-plane Josephson plasma mode, whose frequency lies in the THz range. However, the high-energy in-plane plasma mode has been considered insensitive to THz pumping. Here, we show that THz driving of both low-frequency and high-frequency plasma waves is possible via a general two-plasmon excitation mechanism. The anisotropy of the Josephson couplings leads to markedly different thermal effects for the out-of-plane and in-plane response, linking in both cases the emergence of non-linear photonics across Tc to the superfluid stiffness. Our results show that THz light pulses represent a preferential knob to selectively drive phase excitations in unconventional superconductors.

Superconductor-like effects in an ac-driven normal Mott-insulating quantum dot array

We study the current response of an AC driven dissipative Mott insulator system, a normal quantum dot array, using an analytical Keldysh field theory approach. Deep in the Mott insulator regime, the nonequilibrium steady state (NESS) response resembles a resistively shunted Josephson array, with a nonequilibrium Mott insulating to conductor transition as the drive frequency {\Omega} is increased. The diamagnetic component of the NESS in the conducting phase is anomalous, implying negative inductance, strikingly reminiscent of the {\eta}-pairing phase of a Josephson array with negative phase stiffness. However in the presence of an additional DC field the signature of supercurrent - Shapiro steps - is completely absent. We interpret these properties as number-phase fluctuation effects shared with Josephson systems rather than superconductivity.

Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model

We analyze the interplay of antiferromagnetism and pairing in the two-dimensional Hubbard model with a moderate repulsive interaction. Coupled charge, magnetic, and pairing fluctuations above the energy scale of spontaneous symmetry breaking are treated by a functional renormalization group flow, while the formation of gaps and order below that scale is treated in mean-field theory. The full frequency dependences of the interaction vertices and gap functions are taken into account. We compute the magnetic and pairing gap functions as a function of doping $p$ and compare with results from a static approximation. In spite of the strong frequency dependences of the effective interactions and of the pairing gap, important physical results from previous static functional renormalization group calculations are confirmed. In particular, there is a sizable doping regime with robust pairing coexisting with N\'eel or incommensurate antiferromagnetism. The critical temperature for magnetic order is interpreted as the pseudogap crossover temperature. Computing the Kosterlitz-Thouless temperature from the superfluid phase stiffness, we obtain a superconducting dome in the $(p,T)$ phase diagram centered around 15% hole doping.