A Body-Nonlinear Green's Function Method with Viscous Dissipation Effects for Large-Amplitude Roll of Floating Bodies

A novel time-domain body-nonlinear Green’s function method is developed for evaluating large-amplitude roll damping of two-dimensional floating bodies with consideration of viscous dissipation effects. In the method, the instantaneous wetted surface of floating bodies is accurately considered, and the viscous dissipation effects are taken into account based on the “fairly perfect fluid” model. As compared to the method based on the existing inviscid body-nonlinear Green’s function, the newly proposed method can give a more accurate damping coefficient of floating bodies rolling on the free surface with large amplitudes according to the numerical tests and comparison with experimental data for a few cases related to ship hull sections with bilge keels

Sudden stoppage of rotor in a thermally driven rotary motor made from double-walled carbon nanotubes

In a thermally driven rotary motor made from double-walled carbon nanotubes, the rotor (inner tube) can be actuated to rotate within the stator (outer tube) when the environmental temperature is high enough. A sudden stoppage of the rotor can occur when the inner tube has been actuated to rotate at a stable high speed. To find the mechanisms of such sudden stoppages, eight motor models with the same rotor but different stators are built and simulated in the canonical NVT ensembles. Numerical results demonstrate that the sudden stoppage of the rotor occurs when the difference between radii is near 0.34 nm at a high environmental temperature. A smaller difference between radii does not imply easier activation of the sudden rotor stoppage. During rotation, the positions and electron density distribution of atoms at the ends of the motor show that a sp(1) bonded atom on the rotor is attracted by the sp(1) atom with the biggest deviation of radial position on the stator, after which they become two sp(2) atoms. The strong bond interaction between the two atoms leads to the loss of rotational speed of the rotor within 1 ps. Hence, the sudden stoppage is attributed to two factors: the deviation of radial position of atoms at the stator's ends and the drastic thermal vibration of atoms on the rotor in rotation. For a stable motor, sudden stoppage could be avoided by reducing deviation of the radial position of atoms at the stator's ends. A nanobrake can be, thus, achieved by adjusting a sp(1) atom at the ends of stator to stop the rotation of rotor quickly.The authors are grateful for financial support from the National Natural-Science-Foundation of China (Grant Nos. 50908190, 11372100)

Transfer-matrix renormalization group study of the spin ladders with cyclic four-spin interactions

The temperature dependence of the specific heat and spin susceptibility of the spin ladders with cyclic four-spin interactions in the rung-singlet phase is explored by making use of the transfer-matrix renormalization group method. The values of spin gap are extracted from the specific heat and susceptibility, respectively. It is found that for different relative strength between interchain and intrachain interactions, the spin gap is approximately linear with the cyclic four-spin interaction in the region far away from the critical point. Furthermore, we show that the dispersion for the one-triplet magnon branch can be obtained by numerically fitting on the partition function.Comment: 7 pages, 7 figures, 1 tabl

Multi-Domain 2.5D Method for Multiple Water Level Hydrodynamics

The mean water surface (interface) under the air cushion of a surface effect ship (SES) or an air cushion supported platform (ACSP) is generally lower than the outside water surface due to the overpressure of the air cushion. To precisely analyze the hydrodynamics under the air cushion, multiple water levels should be considered in numerical models. However, when using free surface Green’s functions as numerical methods, the water level difference cannot be taken into account, because free surface Green’s functions normally require users to set in the whole water domain a unique datum water surface that completely separates the air domain and the water domain. To overcome this difficulty, a multi-domain approach is incorporated into a 2.5D method that is based on a time domain free surface Green’s function with viscous dissipation effects in this paper. In the novel multi-domain 2.5D method, the water domain is partitioned into inner and outer domains, and the interface is located in the inner domain while the outside water surface is placed in the outer domain. In each domain there exists only one unique water level, while water levels in different domains are allowed to be different. Benefited from this characteristic, the multi-domain 2.5D method is able to precisely consider the water level difference and its influence on hydrodynamics. The newly proposed multi-domain 2.5D method is employed to predict the hydrodynamics of an SES, and it is confirmed that the multi-domain 2.5D method can give better numerical results than the single-domain one for the given case

A study on hydrodynamics of the air cushion of a high-speed PACSCAT

This paper presents an approximate but efficient method for modeling the hydrodynamics and seakeeping performance of partial air cushion supported catamaran (PACSCAT) with planing demihulls. This method takes into account of the effects of the waves on the air–water interface under the air cushion induced by the pulsating pressure in the cushion and by the demihulls, which are ignored by existing approximate methods. Specifically, the new developments are made in two aspects. One is that the governing equations of the heave and pitch motions of the PACSCAT are derived to include the effects of the waves under the air cushion due to the pulsating pressure and the demihulls. Another one is that an approximate method is developed for evaluating the waves due to the pulsating pressure. Better agreement between the experimental data and the numerical results for pressure is achieved

Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.Comment: 6 pages, 9 figures, published versio

Numerical study on the quantitative error of the Korteweg-de Vries equation for modelling random waves on large scale in shallow water

The Korteweg–de Vries (KdV) equation is often adopted to simulate phase-resolved random waves on large scale in shallow water. It shows that the KdV equation is computationally efficient and can give sufficiently accurate results, but it is not always suitable and the error by using it cannot be predicted. This paper attempts to give the quantitative formulas for estimating the error of the statistics when simulating random waves in shallow water by using it. The formulas are obtained by fitting the errors of the KdV equation in comparison with the fully nonlinear model using the same initial condition based on the Wallops spectrum with a wide range of parameters. This paper also demonstrates how the formulas would be used, e.g., to estimate the error of the results by using the KdV model, or to justify its suitability for modelling random waves on large scale in shallow water