Interactions between two touching spherical particles in sedimentation.

A contact of a falling spherical particle with another fixed one in an unbounded viscous fluid is theoretically investigated based on a model of adding the contact interaction to the gravitational and hydrodynamic forces. The hydrodynamic interaction between the two particles is dealt with using an extended successive reflection method, with which the complete solution to the exterior velocity field around the two-particle system is constructed on the basis of the general expression given by Lamb, and then the hydrodynamic forces and torques on the two particles are obtained by integrating the fluid stress over each particle surface. The mechanical contact force is characterized by the standard friction theory with a criterion responsible for the transition from pure rolling to rolling with slip. Resorting to the dynamical equations of motion including the gravitational, hydrodynamic, and contact forces, the settling motion of a spherical particle in the vicinity of another fixed one is depicted using the fourth-order Runge-Kutta-Fehlberg method. Compared with the experimental results available in the literature, the theoretical prediction confirms two moving patterns at contact: pure rolling and rolling with slip, analyzes the dependence of the transition from one to another on the static friction coefficient and the contact separation distance between the particle surfaces, and accounts for a limitation of the quasisteady description of two interacting noncolloidal particles.

Maxwell's demon and Smoluchowski's trap door.

A simulation has been performed to reveal the detailed dynamics and statistical behavior of a Maxwell demon of the simplest kind, a trap door held over by a spring inside a box filled with gas molecules. The role of such a demon can be controlled by tuning Smoluchowski's fluctuations. When the demon is in thermal equilibrium with the rest of the system, it fails to function as designed, and when it is separately subjected to a thermal bath with a different temperature, it creates a temperature or density gradient between the two chambers of the box it divides. As a Maxwell demon, the trap-door device creates more readily a density gradient than that of temperature.

The oscillatory characteristics of a 2C60/CNT oscillator system.

The authors have studied, using molecular dynamic (MD) simulations, the oscillatory characteristics of a 2C60/CNT oscillator system, in which two C60 fullerenes oscillate inside a single walled carbon nanotube (CNT) in two basic modes, i.e., the symmetric and non-symmetric motions. In the symmetric mode, with each oscillation the two fullerenes move symmetrically from the CNT ends towards the CNT center where they bounce off each other and head back towards the ends. In the non-symmetric mode, the two fullerenes move back and forth inside the CNT crossing the center point of the CNT together with each oscillation. The simulations show that the non-symmetric oscillation mode is stable for the prescribed initial (maximum) velocities up to 300 m/s, while the symmetric oscillation mode however, experiences dynamic instabilities for a prescribed initial (maximum) velocity larger than 250 m/s. The instability takes place as a result of the transfer of energy from the translational to the rotational motion of the fullerenes. This characteristic differentiates 2C60/CNT oscillators from double-walled CNT oscillators. The rotation is primarily caused by the inter-colliding of the two fullerenes, which subjects the fullerenes to large van der Waals repelling forces. These repelling forces are not necessarily aligned perfectly along the CNT axis nor precisely pointing towards the mass centers of the fullerenes. These misalignments cause the fullerenes to rock around the CNT's axis, while their offsets from the mass centers cause the fullerenes to rotate. The rocking motion, being severely confined by the CNT, does not gain much energy itself, but instead, channels energy from translational to rotational motion. The energy channeling is found to be reversed in some very short time intervals, but the rotational motion always gains energies from the translational motion over a time interval that is long enough at the MD time scale. This feature, contrary to our experiences in the macroscopic world, appears to be unique for such nanoscopic mechanical systems.

Prediction of aortic augmentation index using radial pulse transmission-wave analysis.

OBJECTIVE: Current arterial transfer functions have low capability in predicting aortic augmentation index (AIx) from radial pulse contour (RPC), because of the difficulty in accurately identifying the merging point (inflection point) in the derived aortic pulse contour (APC). We hypothesize that the formation time between each characteristic wave in APC is about one-third of ejection duration (ED/3). We sought to assess the accuracy of ED/3 in identifying the merging point in APC as compared to the conventional differential method. In addition, we sought to derive the AIx from RPC based on an arterial transfer function and the ED/3 method. METHODS: APC and RPC sequences were measured digitally and simultaneously in 60 subjects (37 males; aged 60 +/- 10 years). An ensemble-averaged RPC-to-APC transfer function was determined from 30 randomly selected subjects and was used to derive APC sequences in the 30 additional subjects. The accuracy of AIx predicted from RPC was determined. RESULTS: In patients with a clearly identifiable merging point in APC, the ED/3 method identified the merging point of measured APC within 1.97 +/- 0.60 ms of that identified by the conventional differential method, with identical AIx. The AIx and merging point of derived APC using the ED/3 method were also within 0.22 +/- 1.01% and 1.81 +/- 1.64 ms, respectively, of those of the measured APC using the conventional differential method. The accuracy of the predicted AIx was independent of age, sex, body-mass index and presence of hypertension. CONCLUSION: In a quiet resting state, the ED/3 is an alternative method for identifying the merging point in APC. In conjunction with transfer-function technique, AIx can be derived accurately from RPC.

Energy exchanges in carbon nanotube oscillators.

Energy exchanges between orderly intertube axial motion and vibrational modes are studied for isolated systems of two coaxial carbon nanotubes at temperatures ranging from 300 to 500 K. It is found that the excess intertube van der Waals energy, depleted from the intertube axial motion, is primarily stored in low-frequency mechanical modes of the oscillator for an extended period of time. This constitutes the first computer simulation of a nanomechanical device that exhibits negative friction.

Unsteady free-surface waves due to a submerged body moving in a viscous fluid.

Unsteady viscous free-surface waves generated by a three-dimensional submerged body moving in an incompressible fluid of infinite depth are investigated analytically. It is assumed that the body experiences a Heaviside step change in velocity at the initial instant. Two categories of the velocity change, (i) from zero to a constant and (ii) from a constant to zero, will be analyzed. The flow is assumed to be laminar and the submerged body is mathematically represented by an Oseenlet. The Green functions for the unbounded unsteady Oseen flows are derived. The solutions in closed integral form for the wave profiles are given. By employing Lighthill's two-stage scheme, the asymptotic representations of free-surface waves in the far wake for large Reynolds numbers are derived. It is shown that the effects of viscosity and submergence depth on the free-surface wave profiles are respectively expressed by the exponential decay factors. Furthermore, the unsteady wave system due to the suddenly starting body consists of two families of steady-state waves and two families of nonstationary waves, which are confined within a finite region. As time increases, the waves move away from the body and the finite region extends to an infinite V-shaped region. It is found that the nonstationary waves are the transient response to the suddenly started motion of the body. The waves due to a suddenly stopping body consist of a transient component only, which vanish as time approaches infinity.