What does head movement tell about the minimum number of mechanical degrees of freedom in quiet human stance?

In this study, we checked experimentally whether anterior–posterior accelerations of the head during quiet human stance are usually below or above known thresholds of the otolith sensor. Thereto, we measured head kinematics with high spatial resolution. Furthermore, we used both these experimental data and computer simulations of two double inverted pendulum (DIP) models in order to verify the validity of DIP models in general. The results are clear cut. First, not only are acceleration thresholds regularly exceeded about once a second but also are velocity thresholds exceeded, albeit probably less frequently. Second, COM and head movement predicted by interwoven DIP model dynamics can not reproduce the mean measured amplitudes at once. Thus, neither the formerly promoted single inverted pendulum nor any DIP model can causally explain the dynamics of quiet human stance. Instead, we suggest to factor in at least three mechanical degrees of freedom. Due to a couple of reasons discussed, the triple inverted pendulum (TIP) model seems to be a promising abstraction implying potential to better understand the dynamics of quiet human stance.     

The load distribution among three legs on the wall: model predictions for cockroaches

In a former study on terrestrial locomotion of cockroaches in the sagittal plane, it was hypothesised that the ground reaction force distribution among three legs synchronously in contact with a substrate is predominantly explained by joint torque minimisation within all three legs. We verified this hypothesis with a simple mechanical model in two dimensions, consisting of one body and three mass-less legs. Hereto, we calculated force distributions resulting from different optimisation criteria for varying slope angles of the substrate. We compared these distributions to each other and the few experimental findings available. We found that, for any slope angle, the force distribution rather seems to be derived from the fundamental “table” solution, i.e. equalised vertical and vanishing horizontal components (equivalent to pure force minimisation at zero slope), than from pure torque minimisation. For cockroaches, the “table” solution is likely to be modified by torque minimisation within the leading and the trailing leg. We demonstrate that the minimisation of leg forces and of interaction forces is fully equivalent. Moreover, our model predicts the force distribution for arbitrary slope angles. Based on our model calculations, we speculate that in terrestrial locomotion, some animals may rely on spring-mass model dynamics whatever slope angle to be overcome. This might only become evident when focusing movement analyses strictly on a gravity rather than on a substrate-based coordinate system.     

Stability of equilibrium for an inverted two-link mathematical pendulum with critical tracking forces

We investigate nonlinear stability for equilibrium of a pendulum with viscoelastic components. The tracking force is chosen so that the matrix of the linearized part of the perturbed motion has two purely imaginary roots or one zero and one negative root. The other two roots are complex with negative real part. The boundary of the domain of stability is divided into “dangerous” and “safe” (in the sense of Bautin) zones. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 100–105, September, 1999.     

A mechanism of transformational plasticity

In order to understand the phenomenon of reversible plasticity exhibited by shape memory alloys and other smart materials, we study an elementary prototypical model. Building on an original idea of Müller and Villaggio [17], we consider an inhomogeneous ensemble of bi-stable elements connected in series and loaded in a soft device. To interpret the fine structure of the hysteresis loops observed experimentally, we assume that the dynamics is maximally dissipative and investigate different evolutiona ry strategies for a “driven” system with external force changing quasi-statically. Our main result is that the inhomogeneity of the elastic properties leads to a distinctive hardening with serrations of a Portevin-Le Chatelier type and produces a realistic memory structure characterized by the “congruency” and “return point memory” properties. Received December 28, 2001 / Published online June 4, 2002 Dedicated to Ingo Müller on the occasion of his 65th birthday Communicated by Kolumban Hutter, Darmstadt     

Amorphous and crystalline states of ultrasoft colloids: a molecular dynamics study

In this work, we study the temperature-induced development of “dynamically arrested” states in dense suspensions of “soft colloids” (multi-arm star polymers and/or block-copolymers micelles) by means of molecular dynamics (MD) simulations. Temperature increase in marginal solvents results in “soft sphere” swelling, dynamical arrest, and eventually crystallization. However, two distinct “dynamically arrested” states were found, one almost amorphous (“glassy”) and one with a considerable degree of crystallinity, yet lower than that of the fully equilibrated crystal. It is remarkable that even that latter state permitted self-diffusion in the timescale of the simulations, an effect that underlies the importance of the “ultra-soft” nature of inter-particle potential. The “number of connections” criterion for crystallinity proved to be very successful in identifying the ultimate thermodynamic trend from the very early stages of the α-relaxation. This paper was presented at the Third Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

Nonlinearly Elastic Shell Models: A Formal Asymptotic Approach I. The Membrane Model

We consider a family of three‐dimensional shells with the same middle surface, all composed of the same nonlinearly elastic Saint Venant‐Kirchhoff material. Using the method of asymptotic expansions with the thickness as the “small” parameter, and making specific assumptions on the applied forces, the geometry of the middle surface, and the kinematic boundary conditions, we show how a “limiting”, “large‐deformation” two‐dimensional model can be identified in this fashion. By linearization, this nonlinear membrane model reduces to the linear membrane model. (Accepted January 13, 1997)     

Increased torque transducer sensitivity via oversampling

The sensitivity of a commercial torque transducer under oscillatory shear conditions is extended by about a factor 3–5 into the small torque region. This increased sensitivity is a result of a straightforward data treatment in the time domain termed “on the fly oversampling”. This method is enabled by the emergence of modern ADC-cards. The underlying ideas of oversampling together with a first experimental verification of this method are described in detail. Received: 22 August 2000 Accepted: 14 November 2000     

Numerical simulation of wave flows caused by a shoreside landslide

A mathematical model is developed for formation and propagation of discontinuous waves caused by sliding of a shoreside landslide into water. The model is based on the equations of a two-layer “shallow liquid” with specially introduced “dry friction” in the low layer, which allows one to describe the joint motion of the landslide and water. An explicit difference scheme approximating these equations is constructed, and it is used to develop a numerical algorithm for simulating the motion of the free boundaries of both the landslide and water (in particular, the propagation of a water wave along a dry channel, incidence of the wave on the lakeside, and flow over obstacles). Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 109–117, July–August, 1999.     

踝关节外骨骼人机耦合动力学与助力性能分析

踝关节在人体下肢运动过程中提供了最大的关节力矩, 因此在下肢增强型外骨骼的研究中, 踝关节外骨骼受到了重点关注. 穿戴外骨骼的人体的行走是典型的动力学问题, 但目前人机耦合动力学的相关研究还处于早期阶段. 本文以绳驱踝关节外骨骼为研究对象, 融合机器人正运动学方法和拉格朗日方程建立了考虑足?地交互力、人体关节力矩和外骨骼力矩的人?机耦合动力学模型. 模型中, 足?地交互力由Kelvin-Voigt模型结合库伦摩擦模型描述, 人体关节力矩由基于粒子群优化的PD控制生成, 外骨骼期望力矩由上层控制器依据人体步态周期确定. 通过基于模型的动力学仿真, 本文从人体踝关节角度、踝关节力矩、踝关节功率和踝关节做功多个角度系统分析了踝关节外骨骼对人体行走的助力效果. 研究表明, 在2.0 km/h到6.5 km/h的人体步行速度下, 穿戴外骨骼可以实现至少24.84%的人体踝关节平均力矩下降和至少24.69%的踝关节做功下降. 本文也开展了基于SCONE平台的肌肉骨骼建模和预测仿真. 仿真结果表明, 在3.6 km/h的步行速度下, 穿戴外骨骼可以有效降低比目鱼肌的激活度峰值, 并使肌电信号的RMS值下降了6.21%, 从而从生理学的角度证实了踝关节外骨骼的助力效果. 本文的结果进一步完善了人体下肢?外骨骼耦合系统的动力学建模和分析方法, 从动力学和生理学角度证实和解释了踝关节外骨骼对行走的助力机制, 也为今后下肢外骨骼的实验研究提供了理论支撑.      

Poroelasticity-I: Governing Equations of the Mechanics of Fluid-Saturated Porous Materials

We present here the approach to the theory of fluid-filled poroelastics based on consideration of poroelastics as a continuum of “macropoints” (representative elementary volumes), which “internal” states can be described by as a set of internal parameters, such as local relative velocity of fluid and solid, density of fluid, internal strain tensor, specific area, and position of the center of mass of porous space. We use the generalized Cauchy–Born hypothesis and suggest that there is a system of (structural) relationships between external parameters, describing the deformation of the continuum and internal parameters, characterizing the state of representative elementary volumes. We show that in nonhomogenous (and, particularly, nonlinear) poroelastics, an interaction force between solid and fluid appears. Because this force is proportional to the gradient of porosity, absent in homogeneous poroelastics, and one can neglect with dynamics of internal degrees of freedom, this force is equivalent to the interaction force, introduced earlier by Nikolaevskiy from phenomenological reasons. At last, we show that developed theory naturally incorporates three mechanisms of energy absorption: visco-inertial Darcy mechanism, “squirt flow” attenuation, and skeleton attenuation.     

Two-group kinetic theory of vehicular traffic

Summary We study a two-group model of vebicular traffic oli a highway which generalizes the Prigogine-Herman model. According to the two-group theory, drivers are divided into “slow” and “fast”. Correspondingly, we introduce a slow and a fast desired distribution representing the program that drivers of each of the two groups wish to follow. We first prove the existence and the uniqueness of a solution belonging to a suitable Banach space by using the theory of semigroups. Then, we indicate some sufficient conditions for the stability of an x and t independent solution.

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Sommario Si generalizza il modello di Prigogine-Herman del traffico automobilistico su un'autostrada, introducendo due gruppi di guidatori: i “lenti” ed i “veloci”. Ognuno dei due gruppi riene caratterizzato da un'opportuna funzione “desiderio”, che traduce i programmi che i guidatori intendono seguire nel corso del loro viaggio. Facendo poi uso della teoria dei semigruppi, si prova l'esistenza e l'unicità di una soluzione appartenente ad un opportuno spazio di Banach e si danno condizioni sufficienti per la stabilità.

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Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica).As the choice of the appropriate model for these problems is still a controversial matter, the Editorial Board welcomes any comment or discussion from the readers.     

Excluded volume effects on the birefringence and stress of dilute polymer solutions in extensional flow

An algorithm is derived for calculating flow-induced birefringence using a bead-spring model with and without excluded volume effects. The simulation results for the bead-spring model compare well with experimental results for stress and birefringence in extensional flows of dilute solutions of polystyrene molecular weight 2 million in a filament-stretching device in both “theta” and “good” solvents (Orr and Sridhar 1999; Sridhar et al. 2000). In a “good” solvent, both stress and birefringence rise much more rapidly with strain than in a “theta” solvent, making extensional rheology a very sensitive indicator of solvent quality. Received: 7 December 1999 Accepted: 23 May 2000     

Effective thermal conductivity of heterogeneous multi-component materials: an SPH implementation

Modeling heat transfer and fluid flow in materials with complicated micro-structures is a major challenge to numerical methods due to their multiscale and multiphysics nature. A relatively novel numerical technique—the meshless smoothed particle hydrodynamics (SPH) method has the potential of making a significant contribution to this research field. In the present SPH modeling effort, a 2D modeling system is devised for the prediction of the effective thermal conductivity in heterogeneous materials containing two or three different components. The microscopic component configuration inside the materials is constructed in the SPH methodology by randomly assigning particles as a certain component to meet the required macroscopic composition. For heterogeneous two-component materials, the effective thermal conductivity predicted by the modified effective medium theory model with the so-called “flexible” factor f equal to 4.5 agrees well with the SPH data. On the basis of a simple “step-process” concept, the effective thermal conductivity of a heterogeneous multi-component material can be derived from the corresponding “degenerate” materials which consist of fewer components.     

Gas-dynamic signs of explosive eruptions of volcanoes. 2. Model of homogeneous-heterogeneous nucleation. Specific features of destruction of the cavitating magma

The dynamics of state of the crystallite-containing magma is studied within the framework of the gas-dynamic model of bubble cavitation. The effect of crystallites on flow evolution is considered for two cases: where the crystallites are cavitation nuclei (homogeneous-heterogeneous nucleation model) and where large clusters of crystallites are formed in the magma in the period between eruptions. In the first case, decompression jumps are demonstrated to arise as early as in the wave precursor; the intensity of these jumps turns out to be sufficient to form a series of discrete zones of nucleation ahead of the front of the main decompression wave. Results of experimental modeling of an explosive eruption with ejection of crystallite clusters (magmatic “bombs”) suggest that a cocurrent flow of the cavitating magma with dynamically varying properties (mean density and viscosity) transforms to an independent unsteady flow whose velocity is greater than the magma flow velocity. Experimental results on modeling the flow structure during the eruption show that coalescence of bubbles in the flow leads to the formation of spatial “slugs” consisting of the gas and particles. This process is analyzed within a combined nucleation model including the two-phase Iordansky-Kogarko-van Wijngaarden model and the model of the “frozen” field of mass velocities in the cavitation zone. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 167–177, March–April, 2009.     

On the Implementation of the Eigenvalue Method for Limit Cycle Determination in Nonlinear Systems

In many practical systems, limit cycles can be predicted with suitable precision by frequency domain methods using describing functions. Within such an approach, limit cycles can be predicted using the “eigenvalue method” [Somieski, G., Nonlinear Dynamics 26(1), 2001, 3–22]. This contribution presents a novel and advantageous implementation of this method, using singular value instead of eigenvalue calculations, and enhancing computational efficiency by avoiding a so called “frequency iteration”. An erratum to this article is available at .     

On variational features of vortex flows

Ideal incompressible fluid is a Hamiltonian system which possesses an infinite number of integrals, the circulations of velocity over closed fluid contours. This allows one to split all the degrees of freedom into the driving ones and the “slave” ones, the latter to be determined by the integrals of motions. The “slave” degrees of freedom correspond to “potential part” of motion, which is driven by vorticity. Elimination of the “slave” degrees of freedom from equations of ideal incompressible fluid yields a closed system of equations for dynamics of vortex lines. This system is also Hamiltonian. The variational principle for this system was found recently (Berdichevsky in Thermodynamics of chaos and order, Addison-Wesly-Longman, Reading, 1997; Kuznetsov and Ruban in JETP Lett 67, 1076–1081, 1998). It looks striking, however. In particular, the fluid motion is set to be compressible, while in the least action principle of fluid mechanics the incompressibility of motion is a built-in property. This striking feature is explained in the paper, and a link between the variational principle of vortex line dynamics and the least action principle is established. Other points made in this paper are concerned with steady motions. Two new variational principles are proposed for steady vortex flows. Their relation to Arnold’s variational principle of steady vortex motion is discussed.      

The effects of casting speed on steel continuous casting process

A three dimensional simulation of molten steel flow, heat transfer and solidification in mold and “secondary cooling zone” of Continuous Casting machine was performed with consideration of standard k−ε model. For this purpose, computational fluid dynamics software, FLUENT was utilized. From the simulation standpoint, the main distinction between this work and preceding ones is that, the phase change process (solidification) and flow (turbulent in mold section and laminar in secondary cooling zone) have been coupled and solved jointly instead of dividing it into “transient heat conduction” and “steady fluid flow” that can lead to more realistic simulation. Determining the appropriate boundary conditions in secondary cooling zone is very complicated because of various forms of heat transfer involved, including natural and forced convection and simultaneous radiation heat transfer. The main objective of this work is to have better understanding of heat transfer and solidification in the continuous casting process. Also, effects of casting speed on heat flux and shell thickness and role of radiation in total heat transfer is discussed.     

Effective Hamiltonians and Averaging for Hamiltonian Dynamics I

This paper, building upon ideas of Mather, Moser, Fathi, E and others, applies PDE (partial differential equation) methods to understand the structure of certain Hamiltonian flows. The main point is that the “cell” or “corrector” PDE, introduced and solved in a weak sense by Lions, Papanicolaou and Varadhan in their study of periodic homogenization for Hamilton-Jacobi equations, formally induces a canonical change of variables, in terms of which the dynamics are trivial. We investigate to what extent this observation can be made rigorous in the case that the Hamiltonian is strictly convex in the momenta, given that the relevant PDE does not usually in fact admit a smooth solution. Accepted October 11, 2000?Published online March 7, 2001     

COMPREHENSIVE MATHEMATICAL MODEL OF MICROCIRCULATORY DYNAMICS (Ⅰ)——BASIC THEORY

Under the basis of physiological data, a nonlinear and unsteady comprehensive mathematical model of microcirculatory dynamics with distributed parameters is developed. Hemodynamics, interstitium dynamics, lymph dynamics, dynamics of protein transport, oxygen dynamics, dynamics of heat transfer, and myogenic and metabolic regulation procedures are included. The interactions between these factors were comprehensively exhibited. The influences of arteriolar vasomotion and nonlinear viscoelasticity of blood in arteriole are considered. A simplified vessel network consisting of arteriole, open and reserved capillaries, venule, initial lymphatics and arteriole-venule anastomose is adopted as the geometrical model. This kind of comprehensive mathematical model is helpful in analyzing clinical data and developing a “numerical experiment method” in microcirculation research.