Few Degrees Of Freedom Research Articles

Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann–Bhatnagar–Gross–Krook equation introduced by the authors [Dzanic et al., J. Comput. Phys. 486, 112146 (2023)], consisting of a highly efficient high-order spatial discretization augmented with a discretely conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e., high spatial resolution) is significantly more important than particle collision (i.e., high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain. These findings suggest that highly accurate spatial schemes (e.g., high-order schemes) are a promising approach for solving molecular gas dynamics for complex flows and that the direct solution of the Boltzmann equation can be performed at a reasonable cost when compared to hydrodynamic simulations at the same level of resolution.

Relation between degrees of collectivity and repetition patterns of quadrupole transition probabilities in the candidates of shape coexistence

In this article, we study the possible relationship between degrees of freedom of collectivity in protons and neutrons' last orbitals and different patterns of quadrupole transition possibilities in the shape coexistence candidates. Because of the dependence of shape coexistence on the arrangement of nucleons in the nuclear structure, we classified the candidates of shape coexistence based on neutrons and protons' last orbitals using the shell-model configuration. In the orbitals corresponding to the neutron numbers in the N=40, 60, and 90 regions, there is a limitation in the degree of freedom for neutrons, and proton-induced shape coexistence occurs. Also, for the orbitals corresponding to the atomic numbers of the Z=40, 52, and 82 regions, the degree of freedom is limited for protons, and neutron-induced coexistence occurs. In this article, we study both the nuclei that belong to the neutron and proton-induced shape coexistence categories and the nuclei that are candidates for shape coexistence but do not belong to the mentioned two categories. The study of different patterns indicates that the |B(E2;22+→01+)−B(E2;21+→01+)|B(E2;21+→01+), |B(E2;22+→01+)−B(E2;41+→21+)|B(E2;41+→21+), |B(E2;22+→01+)−B(E2;61+→41+)|B(E2;61+→41+), |B(E2;23+→01+)−B(E2;21+→01+)|B(E2;21+→01+), |B(E2;23+→01+)−B(E2;41+→21+)|B(E2;41+→21+), and |B(E2;23+→01+)−B(E2;61+→41+)|B(E2;61+→41+) follow a similar repetition range)in most cases(for ratios related to the neutrons and protons' last orbitals classification. Also, in addition to the mentioned transition possibilities, in transitions related to the neutrons' last orbitals classification, the |B(E2;23+→21+)−B(E2;41+→21+)|B(E2;41+→21+) and |B(E2;23+→21+)−B(E2;61+→41+)|B(E2;61+→41+) have a repetition pattern. In the orbitals where neutrons and protons have fewer degrees of freedom (proton and neutron-induced shape coexistence occurs), the results show that the data related to repetition patterns are less correlated than in other orbitals. The study includes information on specific Nilsson orbitals, which are crucial in investigations related to shape coexistence. Correlating observations to these orbitals allows for a more accurate representation of the underlying microscopic picture, enhancing the quality of analysis and strengthening the connection between observations and the SC phenomenon.

Dynamic response analysis for bridges subjected to moving vehicle loads by using the analytical dynamic stiffness method

This paper presents a highly efficient and accurate analytical method for the dynamic analysis of subjected to moving loads. Bridges with complex cross section and considering damping are modelled as plate built-up structures by the dynamic stiffness method with few degrees of freedom. Different moving loads with time-varying amplitudes travelling at different speeds can be modelled semi-analytically: The moving vehicle loads with varying amplitude are transformed into the frequency-wavenumber domain by the analytical sine transform combined with the fast Fourier transform; then the time-spatial domain dynamic response of the bridge is computed by the associated inverse transforms from the frequency-wavenumber domain response of the dynamic stiffness model. The most commonly used box girder railway bridge is taken as an example, and the results of both free vibration and dynamic response subject to moving train wheel loads computed by the proposed method are validated well by the finite element software ANSYS. The proposed method uses about 1.2% time of that taken by the ANSYS but achieves a similar level of accuracy. The proposed method can serve as an efficient alternative tool of modal and dynamic response analysis for the design and optimization of a wide range of complex bridges.

An efficient local moving thermal-fluid framework for accelerating heat and mass transfer simulation during welding and additive manufacturing processes

Numerical prediction of melt pool morphology and temperature distribution of thermomechanical processes (welding, additive manufacturing) plays an important role in understanding the relationships between process parameters and the quality of manufactured parts. The heat conduction models are limited in their predictability because the transport phenomena relevant to the melt pool dynamic are ignored. In contrast, the multiphysics model allows consideration of the heat transfer, free surface evolution, and transport phenomena in the melt pool, leading to more accurate predictions. However, the computational cost of multiphysics models makes them impractical for part-scale simulations. In this paper, a local moving thermal-fluid framework based on the finite element method is presented, which allows solving the thermal-fluid problem only in the small moving zone containing the melt pool and the heat transfer problem in the rest part. Therefore, this new proposed moving thermal-fluid (MTF) framework is predictive as well as the full thermal-fluid model, while it is much more efficient than a full thermal-fluid model since there are much fewer degrees of freedom (DOF) to solve. Finally, numerical validation tests in welding and additive manufacturing simulations highlight its computational efficiency and high-fidelity, and a relative error of less than 2.6% was observed in predicting melting pool dimensions compared to full thermal-fluid model. In the part-scale simulation of laser welding benchmark, the MTF model takes only 62 h in place of about three weeks required by a full thermal-fluid model.

Analysis and Synthesis of Digital Dyadic Sequences

We explore the space of matrix-generated (0, m , 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a complete characterization of the design space and count the possible number of constructions with and without considering possible reorderings of the point set. Based on this analysis, we then show that every digital dyadic net can be reordered into a sequence, together with a corresponding algorithm. Finally, we present a novel family of self-similar digital dyadic sequences, to be named ξ -sequences, that spans a subspace with fewer degrees of freedom. Those ξ -sequences are extremely efficient to sample and compute, and we demonstrate their advantages over the classic Sobol (0, 2)-sequence.

Superstatistical analysis of sea surface currents in the Gulf of Trieste, measured by high-frequency radar, and its relation to wind regimes using the maximum-entropy principle

Abstract. Two years (2021–2022) of high-frequency-radar (HFR) sea surface current data in the Gulf of Trieste (northern Adriatic Sea) are analysed. Two different timescales are extracted using a superstatistical formalism: a relaxation time and a larger timescale over which the system is Gaussian. We propose obtaining an ocean current probability density function (PDF) combining (i) a Gaussian PDF for the fast fluctuations and (ii) a convolution of exponential PDFs for the slowly evolving variance of the Gaussian function rather than for the thermodynamic β=1/σ2 in a system with a few degrees of freedom, as the latter has divergent moments. The Gaussian PDF reflects the entropy maximization for real-valued variables with a given variance. On the other hand, if a positive variable, as a variance, has a specified mean, the maximum-entropy solution is an exponential PDF. In our case the system has 2 degrees of freedom, and therefore the PDF of the variance is the convolution of two exponentials. In the Gulf of Trieste there are three distinct main wind forcing regimes: bora, sirocco, and low wind, leading to a succession of different sea current dynamics on different timescales. The universality class PDF successfully fits the observed data over the 2 observation years and also for each wind regime separately with a different variance of the variance PDF, which is the only free parameter in all the fits.

A variational approach to effective models for inelastic systems

Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system’s mechanical response. However, for large systems this procedure can quickly become computationally overwhelming, especially in three-dimensions when the microstructure is locally complex. In such settings multi-scale modeling offers a route to a more efficient model by holding out the promise of a framework with fewer degrees of freedom, which at the same time faithfully represents, up to a certain scale, the behavior of the system. In this paper, we present a methodology that produces such models for inelastic systems upon the basis of a variational scheme. The essence of the scheme is the construction of a variational statement for the free energy as well as the dissipation potential for a coarse scale model in terms of the free energy and dissipation functions of the fine scale model. From the coarse scale energy and dissipation we can then generate coarse scale material models that are computationally far more efficient than either directly solving the fine scale model or by resorting to FE2 type modeling. Moreover, the coarse scale model preserves the essential mathematical structure of the fine scale model. An essential feature for such schemes is the proper definition of the coarse scale inelastic variables. By way of concrete examples, we illustrate the needed steps to generate successful models via application to problems in classical plasticity, included are comparisons to direct numerical simulations of the microstructure to illustrate the accuracy of the proposed methodology.

Grounded source transient electromagnetic 3D forward modeling with the spectral-element method and its application in hydraulic fracturing monitoring

A long wire with large current source transient electromagnetic (TEM) monitoring, with a large detection depth, low cost, safety, and environmental protection, has unique advantages in the testing and identification of unconventional reservoir fluid and the evaluation of stimulated reservoir volume. So, the TEM 3D forward modeling method has become a research hotspot. Although the finite-element method (FEM) is a type of numerical algorithm that has been widely applied in three-dimensional (3D) electromagnetic field forward modeling, the efficiency and accuracy of FEM require further improvement in order to meet the demand of fast 3D inversion. By increasing the order of the basis function and adjusting the principle of mesh discretization, the precision of the mixed-order spectral-element (SEM) result will be increased. The backward Euler scheme is an unconditionally stable technique which can ignore the impact of the scale of the time step. To achieve a better description of the nonlinear electromagnetic (EM) response of the grounded source TEM method and to optimize the efficiency and accuracy/precision of the 3D TEM forward modeling method significantly, we proposed the use of 3D TEM forward modeling based on the mixed-order SEM and the backward Euler scheme, which can obtain more accurate EM results with fewer degrees of freedom. To check its accuracy and efficiency, the 1D and 3D layered models are applied to compare the SEM results with the semi-analytical and FEM solutions. In addition, we analyzed the accuracy and efficiency of the SEM method for different types of order basis functions. Finally, we calculated the long-wire source TEM response for a practical 3D earth model of a shale gas reservoir for fracturing monitoring and tested the feasibility of the TEM method in a hydraulic fracturing monitoring area to further demonstrate the flexibility of the SEM method.

The s-version finite element method for non-linear material problems

This study intended to extend the s-version of the finite element method (s-version FEM) to cope with elastic–plastic problems. Compared with the conventional FEM, the s-version FEM, which overlays a set of local mesh with fine element size representing irregular features over the conventional FE mesh with coarse element size, can considerably simplify issues in domain discretisation with fewer degrees of freedom and provide accurate numerical predictions. However, most applications of the s-version FEM were limited to elastic problems only, leaving its applications to elastic–plastic problems almost blank owing to insufficient instructions on stress update when plasticity sets in. To address these issues, detailed instructions and formulations to cope with plasticity problems with the s-version FEM were presented for its first time. The recursive element subdivision technique was implemented to generalise its application where local elements intersect with global element edges. A 3D stress concentration problem with linear/non-linear material properties was analysed; their numerical results were compared with the exact solutions and those obtained from the conventional FEM with very fine elements. The comparison highlights the flexibility of the s-version FEM in domain discretisation and its superior accuracy in numerical calculations, thereby exhibiting high potential applications in structural integrity assessment with complex structures, geometric defects, and material non-linearity.

A Review of Research on Upper Extremity Rehabilitation Robots

Background:: Most of the patients with limb paralysis caused by stroke and traumatic brain injury are unable to take care of themselves, which not only causes great physical and psychological stress to the patients but also poses a heavy burden on their families and society. The global population is entering the aging phase. The number and proportion of older people is increasing in almost every country in the world. Population aging has the potential to become one of the most important social trends of the 21st century, and almost all areas of society are affected by it, including labor and financial markets, demand for goods and services, such as housing, transportation, and social security, family structures, and intergenerational relationships. Rehabilitation robotics is a research field that has emerged from this demand. Objective:: Through the analysis of the current situation and development of upper limb rehabilitation robots, several types of upper limb rehabilitation robots with the most widely used structures today are extracted from the representative results, and each robot is analyzed and elaborated in detail. It provides a reference for readers to choose the appropriate upper limb rehabilitation robots. Methods:: We have classified the upper limb rehabilitation robots through several patents, briefly explained and analyzed the robots grouped, summarized the advantages and disadvantages of various robots, and provided an outlook on future development trends. Results:: Through the research and analysis of the degree of freedom and control system of the upper limb rehabilitation robot, it can be seen that certain upper limb rehabilitation robots have large structures and complex systems, and their application scope is limited; most domestic rehabilitation robots have fewer degrees of freedom and can only provide rehabilitation training for single joints or a few degrees of freedom, especially for the shoulder, which has a small spatial range, too low range of motion and amplitude, and a single mode of motion, and cannot complete a wide range of motion for certain joints, as well as a compound motion for multiple joints, thus failing to provide adequate stimulation of the central nerve. Conclusion:: The analysis shows that the existing upper limb rehabilitation robots are poorly adaptable and not well-suited for situations, such as for different patients and different recovery periods of the same patient. The upper limb rehabilitation robot solution needs to be more appropriately designed to meet all requirements in the rehabilitation movement of patients.

Rational design of high performance metal organic framework stationary phase for gas chromatography

Metal organic frameworks (MOFs) are assembled from metal ions or clusters and organic ligands. The high tunability of these components offers a solid structural foundation for achieving efficient gas chromatography (GC) separation. This review demonstrates that the design of high performance MOFs with suitable stationarity should consider both the thermodynamic interactions provided by these MOFs and the kinetic diffusion of analytes. Thermodynamic parameters are basic indicators for describing the interactions between various analytes and the stationary phase. Thermodynamic parameters such as retention factors, McReynolds constants, enthalpy changes, and entropy changes can reflect the relative intensity of thermodynamic interactions. For example, a larger enthalpy change indicates a stronger thermodynamic interaction between the analytes and stationary phase, whereas a smaller enthalpy change indicates a weaker interaction. In addition, the degree of entropy change reflects the relative degrees of freedom of analytes in the stationary phase. A larger entropy change indicates that the analytes have fewer degrees of freedom in the stationary phase. The higher the degree of restriction, the closer the adsorption of the analytes and, thus, the longer the retention time. Thermodynamic interactions, such as metal affinity, π-π interactions, polarity, and chiral sites, can be rationally introduced into MOF structures by pre- or post-modifications depending on the target analytes. These tailored thermodynamic interactions create a favorable environment with subtle differences for efficient analyte separation. For example, MOF stationarity may require large conjugation centers to provide specific π-π interactions to separate benzenes. Chiral groups may be required in the MOF structure to provide sufficient interactions to separate chiral isomers. The kinetic diffusion rate of the analytes is another critical factor that affects the separation performance of MOFs. The diffusion coefficients of analytes in the stationary phase (Ds) can be used to evaluate their diffusion rates. The chromatographic dynamics equation illustrates that the chromatographic peak of analytes tends to be sharper and more symmetrical when the Ds is large, whereas a wider trailing peak may appear when the Ds is small. The Van Deemter equation also proves that a low Ds may lead to a high theoretical plate height and low column efficiency, whereas a high Ds may lead to a low theoretical plate height and increased column efficiency. Analyte diffusion can be significantly influenced by the pore size, shape, particle size, and packing mode of MOFs. For instance, an excessively small pore size results in increased mass transfer resistance, which affects the diffusion of analytes in the stationary phase, probably leading to serious peak trailing. Thus, a suitable pore size is required to enhance the kinetic diffusion of analytes and improve the separation performance of MOFs. Theoretically, the design of a high performance MOF stationary phase requires the creation of routes for the rapid diffusion of analytes. However, the separation ability of an MOF is determined by not only the kinetic diffusion rate of the analytes but also the thermodynamic interactions it provides. An excessively fast diffusion rate may lead to insufficient interactions between the analytes and MOFs, compromising their ability to effectively separate different analytes. The thermodynamic interactions and kinetic diffusion of analytes are synergistic and mutually essential. Therefore, this review concludes with research on the influence of both the thermodynamic interactions and kinetic diffusion of analytes on the performance of MOF stationary phases. Based on the findings of this review, we propose that high performance MOF stationary phases can be achieved by balancing the thermodynamic interactions and kinetic diffusion of analytes in these phases through the rational design of the MOF structure. We believe that this review provides useful guidelines for the design of high performance MOF stationary phases.

Design and optimization of kirigami-inspired rotational parabolic deployable structures

Deployable structures designed through diverse methodologies have become crucial in contemporary engineering applications. Despite their distinct advantages, the exploration of kirigami techniques for designing parabolic deployable structures remains nascent. In this study, we explored the potential of kirigami for developing a parabolic deployable structure with a large deployment ratio and few degrees of freedom. According to the plane-symmetric kirigami pattern endowed with thickness, two distinctive deployable structural configurations were introduced. Based on these configurations, a geometric model and corresponding optimization method were proposed. A rigorous analysis was conducted to examine the effects of the array number and array row number on the deployment ratio. Finally, the deployment ability of the designed parabolic deployable structure and the surface morphology of the paraboloid were evaluated through computational simulations and prototype manufacturing. The results indicated that the kirigami-inspired deployable structure had an excellent deployment ability and closeness to the aimed paraboloid. This study provides an innovative methodology for designing curved deployable structures for engineering applications.

A new approach to evaluating loop inconsistency in network meta-analysis.

In network meta-analysis, studies evaluating multiple treatment comparisons are modeled simultaneously, and estimation is informed by a combination of direct and indirect evidence. Network meta-analysis relies on an assumption of consistency, meaning that direct and indirect evidence should agree for each treatment comparison. Here we propose new local and global tests for inconsistency and demonstrate their application to three example networks. Because inconsistency is a property of a loop of treatments in the network meta-analysis, we locate the local test in a loop. We define a model with one inconsistency parameter that can be interpreted as loop inconsistency. The model builds on the existing ideas of node-splitting and side-splitting in network meta-analysis. To provide a global test for inconsistency, we extend the model across multiple independent loops with one degree of freedom per loop. We develop a new algorithm for identifying independent loops within a network meta-analysis. Our proposed models handle treatments symmetrically, locate inconsistency in loops rather than in nodes or treatment comparisons, and are invariant to choice of reference treatment, making the results less dependent on model parameterization. For testing global inconsistency in network meta-analysis, our global model uses fewer degrees of freedom than the existing design-by-treatment interaction approach and has the potential to increase power. To illustrate our methods, we fit the models to three network meta-analyses varying in size and complexity. Local and global tests for inconsistency are performed and we demonstrate that the global model is invariant to choice of independent loops.

A spatial local method for solving 2D and 3D advection-diffusion equations

PurposeThis study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.Design/methodology/approachThe parabolic AD equations are reduced to the nonhomogeneous elliptic system of partial differential equations by utilizing the Chebyshev spectral collocation method (ChSCM) in the temporal variable. The implicit-explicit local differential transform method (IELDTM) is constructed over two- and three-dimensional meshes using continuity equations of the neighbor representations with either explicit or implicit forms in related directions. The IELDTM yields an overdetermined or underdetermined system of algebraic equations solved in the least square sense.FindingsThe IELDTM has proven to have excellent convergence properties by experimentally illustrating both h-refinement and p-refinement outcomes. A distinctive feature of the IELDTM over the existing numerical techniques is optimizing the local spatial degrees of freedom. It has been proven that the IELDTM provides more accurate results with far fewer degrees of freedom than the finite difference, finite element and spectral methods.Originality/valueThis study shows the derivation, applicability and performance of the IELDTM for solving 2D and 3D advection-diffusion equations. It has been demonstrated that the IELDTM can be a competitive numerical method for addressing high-space dimensional-parabolic partial differential equations (PDEs) arising in various fields of science and engineering. The novel ChSCM-IELDTM hybridization has been proven to have distinct advantages, such as continuous utilization of time integration and optimized formulation of spatial approximations. Furthermore, the novel ChSCM-IELDTM hybridization can be adapted to address various other types of PDEs by modifying the theoretical derivation accordingly.

Flexible instrument with contact-aided structure and force feedback for endoscopic surgery.

Robot-assisted surgery can effectively reduce the difficulty and improve the success rate of the surgeries. However, currently available flexible instruments have several limitations, such as large size, few degrees of freedom, and lack of contact force perception. This study proposes a master-slave flexible instrument capable of force feedback. The instrument has a maximum outer diameter of 3mm and an overall length of 1200mm. With the internal working channel unoccupied, a three-dimensional force sensing unit is designed based on the neural network. The corresponding master-slave control method with proportional force feedback was also designed to effectively control the instrument. To verify the effectiveness of the system, in vitro and in vivo experiments were conducted. The corresponding tasks were successfully completed. The animal trial conducted in the digestive tract of a live swine proved that the system has the potential for clinical use.

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. We show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

Adaptive quadtree polygonal based edge-based smoothed finite element method for quasi-incompressible hyperelastic solids

This paper discusses an adaptive framework based on the edge-based strain smoothing approach with polygonal meshes for largely deformable quasi-incompressible hyperelasticity. The proposed approach employs the quadtree decomposition for spatial discretization and the strain smoothing technique to compute the bilinear/linear form. The local refinement is based on the stress distribution and the element that has hanging nodes due to adaptive local refinement are treated as polygonal element within the strain smoothing framework. The accuracy and the robustness of the proposed framework are numerically studied with a few examples. When compared to uniform refinement, it is seen that the proposed framework yields comparable results with fewer degrees of freedom.

Modeling strategy and dynamic analysis of a dual-rotor-bearing-casing system in aero-engine

In this study, a novel modeling method for a dual-rotor-bearing-casing system is proposed based on the finite element method (FEM) and the model reduction method. The dual-rotor system is modeled using Timoshenko beam and rigid disc elements, while the casing is modeled using shell elements. To reduce the number of degrees of freedom (DOFs), the modified Craig–Bampton method is used to downscale the finite element model of the casing. In addition, the Hertzian contact force and the DOFs of the bearing outer race and pedestal are considered in the bearing model. Through a specific assembly method, a dynamic model of the dual-rotor-bearing-casing is established at the expense of slight increase in the number of DOFs. Based on this dynamic model with fewer DOFs, the effects of two disc imbalances and the rub-impact fault between the low-pressure (LP) turbine and casing are then introduced as an application of the proposed model. The calculation results indicate that the critical speeds of each order of the whole aero-engine model are significantly lower than those of the casing-free model. In the amplitude-frequency diagram, the peak of the critical speed of the whole aero-engine model is found to appear earlier, and the extent of rightward bending is larger. The study also includes parametric analysis to examine the effects of parameters such as the coefficient of friction, the casing-disc contact stiffness, and the casing-foundation connection stiffness. After introducing the nonlinear bearing model, a large number of fractional frequency components are found in the frequency-domain diagram, the dynamic characteristics of the model become more complicated. The coupled bending-torsional effect has also been studied in detail, the calculation results show that it is reasonable to ignore the torsional deformation.

A syntactic analysis of a complex motor action: the octopus arm ‘slap’

The analysis of a natural motor action is always difficult, especially when different motor programs are combined within the same interaction with the environment. We analyzed the behavior of an octopus, Abdopus sp., filmed in tidal pools in Okinawa, Japan, which used the kinematic primitives of rotation and translation of its hydrostatic arms, and combined these kinematic behaviors serially and in parallel to ‘slap’ at fish in the wild. In total, 19 slaps were analyzed. The kinematics of arm movement were measured in both external and animal-centered reference frames, while the octopus was slapping at the fish. By combining these primitives, the octopus is able to maintain flexibility while controlling only a few degrees of freedom, a concept we term ‘flexible rigidity’. This slapping action supports Flash and Hochner’s embodied organization view of motor behavior, as well as their idea that motor primitives can combine syntactically to form a complex action. The octopus’s ability to use sensory feedback from the position of a moving fish target, along with the feed-forward motor primitives, allows for the building of complex actions at dynamic equilibrium with the environment. Over all, these findings lead to a more realistic view of how a complex behavior allows an animal to coordinate with its environment.

Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold.

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultraviolet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.