Torsion balances with fibres of zero length

Torsion balances have good immunity to tilt and low rotational stiffness. However precise control of the position of the suspended torsion ‘bob’ is difficult in the presence of ground vibrations and tilt and this is a limiting factor in applications where Casimir forces or putative non-Newtonian short-range forces are being measured. We describe how the desirable characteristics of torsion balances can be reproduced in a rigid body that is suspended using applied forces rather than a torsion fibre. The suspension system can then provide a more precise control of the degrees of freedom of the suspended body. We apply these ideas to a superconducting levitated torsion balance, developed by the authors, and a generic electrostatic suspension. We present results of preliminary experiments that provide support for our analyses.     

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of non-linear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two-bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead-lag, elastic bending in flap and lead-lag, blade root torsion, and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated by using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.     

非完整映射理论与刚体定点转动的几何描述

利用非完整映射方法,从一个已知Riemann空间构造一个嵌入其中的Riemann-Cartan空间.作为特例,研究从Euclidean空间构造Weitzenbock空间的方法.基于dAlembert-Lagrange原理和非完整映射,将一个Riemann空间的测地线对应于另一个Riemann-Cartan空间的自平行线.把这种非完整映射理论应用到刚体定点转动问题上,得到了刚体运动的欧拉方程是欧拉角描述的Riemann位形空间的测地线方程,而在刚体角速度对应的准坐标空间上是常挠率Riemann-Cartan空间的自平行线方程的结论. 关键词： 欧拉角 非完整映射 Riemann-Cartan空间 自平行线     

CORCEMA refinement of the bound ligand conformation within the protein binding pocket in reversibly forming weak complexes using STD-NMR intensities

We describe an intensity-restrained optimization procedure for refining approximate structures of ligands within the protein binding pockets using STD-NMR intensity data on reversibly forming weak complexes. In this approach, the global minimum for the bound-ligand conformation is obtained by a hybrid structure refinement method involving CORCEMA calculation of intensities and simulated annealing optimization of torsion angles of the bound ligand using STD-NMR intensities as experimental constraints and the NOE R-factor as the pseudo-energy function to be minimized. This method is illustrated using simulated STD data sets for typical carbohydrate and peptide ligands. Our procedure also allows for the optimization of side chain torsion angles of protein residues within the binding pocket. This procedure is useful in refining and improving initial models based on crystallography or computer docking or other algorithms to generate models for the bound ligand (e.g., a lead compound) within the protein binding pocket compatible with solution STD-NMR data. This method may facilitate structure-based drug design efforts.     

Effect of Torsion on Cisplatin-Induced DNA Condensation

We investigate the effect of torsion on DNA condensation with the covalently closed circular DNA as the torsionconstrained system, using an atomic force microscope. It is found that there are two stages in the DNA condensation process under torsional constraint. At the early stage, the low torsion will accelerate DNA condensation by promoting the formation of micro-loops or intersection structures; while at the later stage, the increasing torsion will slow it down by preventing the crosslinking of cisplatin and DNA since the DNA molecule becomes more rigid. Our results show the important role of torsion in DNA condensation and sheds new light on the mechanism for DNA condensation.     

Reference motion in deformable bodies under rigid body motion and vibration. Part II: evaluation of the coefficient of restitution for impacts

The dynamic analysis of rigid body impacts is usually performed by using the coefficient of restitution as a measure of the mechanical energy lost in the process. The coefficient of restitution provides an algebraic equation that allows impulse-momentum balance equations to be solved. This paper reports a method for calculating the kinematic coefficient of restitution for the impact of deformable bodies by using a numerical simulation procedure. Calculations were done within the framework of the floating reference frame approach. As shown here for the first time, discriminating between reference velocities and rigid body equivalent velocities is essential with a view to accurately calculating the kinematic coefficient of restitution. Thus, the velocities at which the contact points approach and depart must be calculated as rigid body equivalent velocities. If references velocities are used instead, the resulting coefficient of restitution lacks physical significance. The proposed method is illustrated with two applications, namely: an axial impact of a rigid body on a deformable rod and a transverse impact of a beam on a fixed stop.     

A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows

A fictitious-domain based formulation for fully resolved simulations of arbitrary shaped, freely moving rigid particles in unsteady flows is presented. The entire fluid–particle domain is assumed to be an incompressible, but variable density, fluid. The numerical method is based on a finite-volume approach on a co-located, Cartesian grid together with a fractional step method for variable density, low-Mach number flows. The flow inside the fluid region is constrained to be divergence-free for an incompressible fluid, whereas the flow inside the particle domain is constrained to undergo rigid body motion. In this approach, the rigid body motion constraint is imposed by avoiding the explicit calculation of distributed Lagrange multipliers and is based upon the formulation developed by Patankar [N. Patankar, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research Annual Research Briefs 2001 (2001) 185–196]. The rigidity constraint is imposed and the rigid body motion (translation and rotational velocity fields) is obtained directly in the context of a two-stage fractional step scheme. The numerical approach is applied to both imposed particle motion and fluid–particle interaction problems involving freely moving particles. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of rigid particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of particle-laden turbulent flows.     

Deformable gyroscope in a non-euclidean space classical,non-relativistic theory

The classical mechanics of structured test particles in a manifold with affine connection is studied. Gyroscopic rotations and homogeneous deformations are taken into account as internal degrees of freedom. Hence, in addition to the orbital motion of the centre of mass, the body undergoes affine rotations about the centre (“affinely-rigid body”). Configurations of particles are described mathematically by linear frames in an underlying manifold (physical space).Symmetries of the theory are discussed and in some special cases the equations of motion are derived. The orbital motion is found to be influenced by internal degrees of freedom which are dynamically coupled to the geometry of the manifold. For example, in a Riemann-Cartan space ([4], [8], [9], [25]), internal degrees of freedom interact with curvature and torsion tensors. Imposing then some holonomic constraints (orthonormal frames only), one gets the theory of test rigid bodies in a curved space with torsion. In a Riemannian case (no torsion) such a theory seems to coincide with non-relativistic (although spatially non-Euclidean) limit of theories studied by Dixon, Künzle, Tulczyjew and Papapetrou [5], [13], [26], [15].As for all standard techniques and notations of differential geometry, we follow mainly Kobayashi-Nomizu [12] and Sternberg [23].     

利用刚体转动惯量实验仪验证转动定律的设计

介绍了设计性实验“利用刚体转动惯量实验仪验证转动定律”.该实验要求学生理解刚体动力学原理;利用实验室现有的仪器,对刚体转动惯量实验仪进行改装;提出新的实验原理,可以对阻力矩进行估测,利用该实验装置验证刚体定轴转动定律.     

Quantum theory on protein folding

The conformational change of biological macromolecule is investigated from the point of quantum transition. A quantum theory on protein folding is proposed. Compared with other dynamical variables such as mobile electrons, chemical bonds and stretching-bending vibrations the molecular torsion has the lowest energy and can be looked as the slow variable of the system. Simultaneously, from the multi-minima property of torsion potential the local conformational states are well defined. Following the idea that the slow variables slave the fast ones and using the nonadiabaticity operator method we deduce the Hamiltonian describing conformational change. It is shown that the influence of fast variables on the macromolecule can fully be taken into account through a phase transformation of slow variable wave function. Starting from the conformation-transition Hamiltonian the nonradiative matrix element was calculated and a general formulas for protein folding rate was deduced. The analytical form of the formula was utilized to study the temperature dependence of protein folding rate and the curious non-Arrhenius temperature relation was interpreted. By using temperature dependence data the multi-torsion correlation was studied. The decoherence time of quantum torsion state is estimated. The proposed folding rate formula gives a unifying approach for the study of a large class problems of biological conformational change.     

A boundary condition capturing immersed interface method for 3D rigid objects in a flow

To simulate the flow around an object, we can replace the object with the fluid enclosed by a singular force. We can then simulate the flow on a fixed domain with a fluid–fluid interface supporting the singular force. In this paper, we present a boundary condition capturing approach to determine the singular force for a 3D rigid object. We apply a discontinuous body force to enforce the rigid motion of the fluid replacing the object and compute the singular force based on the kinematics of the object. Due to the singular force and the body force, the flow is not smooth across the interface. We solve the flow using the immersed interface method. Our boundary condition capturing immersed interface method is very efficient and stable, and its accuracy based on the infinity norm is near second order for the velocity and above first order for the pressure.     

Evaluation of helical magnetoelastic anisotropy in Fe-based amorphous wire from the decomposed susceptibility spectra

A novel method is introduced here to evaluate the intrinsic magnetic anisotropy from susceptibility spectra. The combination of two techniques namely, the decomposition of susceptibility spectra together with its dependence on applied torsion is employed to determine quantitatively the intrinsic helical anisotropy in an amorphous wire. The susceptibility spectra of Fe_77.5Si_7.5B₁₅ amorphous wires have been experimentally measured as a function of torsion. The reversible susceptibility is ascribed to wall motion of axial domains within the core, and to magnetization rotation within radial domains in the shell. The relaxation frequencies of these magnetization processes are evaluated to be 0.36 and 1.82 MHz, respectively. The static rotational susceptibility shows an asymmetric behavior with regards to positive and negative torsion angles, and is maximum at the torsion angle of 30°, which counterbalances the internal stress. Present results indicate the existence of an intrinsic helical anisotropy corresponding to an average helical stress of 33 MPa.     

Rotordynamical simulations of a fibre refiner during production

A key component in panel board production is the refiner, whose task is to break raw cellulose wood chips into slender fibres, done by a relative angular motion between stator and rotor. The main problem in predicting the dynamics of these machines is to model the complicated fibre breaking process, since the refining process leads to a three-phase flow (solid wood, water and steam) between the stator and rotor. By modelling the rotor as a rigid body, the process can only contribute by a resulting force and a resulting moment. Through this approach and axial force measurements, it has been shown that the refining process can be treated as a time dependent stiffness matrix and external load. The objective for this paper is to predict and explain dynamical characteristics of fibre refiners during production in such a way that the results can be used already at early stages of the product development process. Two different pressure distribution cases are studied, i.e. one axisymmetric with only radial variations and one non-axisymmetric. It is found that the axisymmetric case only excited forward modes, while the non-axisymmetric case excited all modes. The time dependent stiffness matrix resulted in unstable domains, but also in stable domains with intermittent high amplitudes.     

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid–fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks.     

Vibration analysis of a new curved beam element

The common practice in developing a locking-free curved beam element is to ensure that its interpolation functions of displacement explicitly satisfy the inextensible bending mode condition for the membrane locking-free instead of the rigid body modes. In this paper, we study the impact of this practice on the dynamic characteristics of a finite element by conducting vibration analysis using our newly developed three-node locking-free curved beam element. In this case, the inextensible bending mode condition is satisfied explicitly, while the rigid body modes are satisfied implicitly to 4th-order accuracy. Numerical and experimental examples show that with the newly developed curved beam element, developed by using the implicit representation of a rigid body mode condition, it is possible to recover the rigid body modes of curved beams with low and medium slenderness ratios. This is even true for cases involving a half-circular element and the vibration of the curved beam is predicted with high accuracy.     

Highly sensitive fiber-optic torsion sensor based on an ultra-long-period fiber grating

A high sensitivity fiber-optic torsion sensor, which can measure twist rate and determine twist direction simultaneously based on a novel ultra-long-period fiber grating (ULPFG) with a period of up to several millimeters, is proposed and demonstrated. Such an ULPFG is fabricated by using the high-frequency CO₂ Laser pulses exposure technique. The unique torsion characteristics of the ULPFG are simply analyzed by using the mode coupling theory and the birefringence effect. The experimental results show that the high order resonant wavelengths of the ULPFG have higher torsion sensitivities, which is several times higher than that of the normal LPFG. In addition, an intensity-type demodulation approach used to realize real-time torsion measurement is proposed and demonstrated based on the edge filtering effect of the ULPFG.     

Description of spinning particle in general relativity using commuting spin variables

A general relativistic extension of a recently proposed model of spinning particle using commuting spin variables is given. The results found earlier in an approach using anticommuting (Grassmannian) variables are reproduced and extended to the case with nonzero torsion. The quantization of the model is performed via Feynman path integral and a discretization procedure is proposed leading to a covariant second-order differential equation for the propagator which in the case with zero torsion can be reduced to general relativistic Dirac equation with δ-function source.     

Structural modeling of proteins by integrating small-angle x-ray scattering data

Elucidating the structure of large biomolecules such as multi-domain proteins or protein complexes is challenging due to their high flexibility in solution. Recently, an "integrative structural biology" approach has been proposed, which aims to determine the protein structure and characterize protein flexibility by combining complementary high- and lowresolution experimental data using computer simulations. Small-angle x-ray scattering(SAXS) is an efficient technique that can yield low-resolution structural information, including protein size and shape. Here, we review computational methods that integrate SAXS with other experimental datasets for structural modeling. Finally, we provide a case study of determination of the structure of a protein complex formed between the tandem SH3 domains in c-Cb1-associated protein and the proline-rich loop in human vinculin.     

An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries

We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains.