Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd.     

First-principle proof of the modified collision boundary conditions for the hard-sphere system

A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.     

Mechanics of stretchable electronics on balloon catheter under extreme deformation

Stretchable electronics has been applied to balloon catheters for high-efficacy ablation, with tactile sensing integrated on the surface, to establish full and conformal contact with the endocardial surface for elimination of the heart sink caused by blood flow around their surfaces. The balloon of the catheter folds into uniform ‘clover’ patterns driven by the pressure mismatch inside (∼vacuum) and outside of the balloon (pressure ∼1 atm). The balloon catheter, on which microelectrodes and interconnects are printed, undergoes extreme mechanical deformation during its inflation and deflation. An analytic solution is obtained for balloon catheter inflation and deflation, which gives analytically the distribution of curvatures and the maximum strain in the microelectrodes and interconnects. The analytic solution is validated by the finite element analysis. It also accounts for the effect of inflated radius, and is very useful to the optimal design of balloon catheter.     

Selection of terms for a CI wavefunction to preserve potential surface features

A cumulative selection procedure for choosing configuration functions for inclusion in CI calculations is described. The objective of the method is to obtain equal energy loss, relative to unselected calculations, for different states and different regions of the potential surface. Results obtained from calculations on the BH molecule indicate an overall advantage in comparison to the threshold selection procedure, particularly with regard to molecular geometry changes.     

Vibrational partition functions for H2O derived from perturbation-theory energy levels

Purely vibrational energy levels and partition functions are calculated using three different potential energy surfaces for the H₂O molecule. Results obtained with perturbation-theory, independent-normal-mode (INM), and harmonic approximations are compared with accurate values. For the cases considered here, the expected improvement that perturbation theory provides over the corresponding harmonic treatment is found to be substantial, while the INM approximation leads to results which are worse than the corresponding harmonic ones. In fact, we show that reliable partition functions for these potential surfaces can be obtained when resonance contributions are removed from the perturbation-theory treatment, and we propose a theoretical criterion for deciding when a particular interaction should be treated as resonant.     

自由基SiH_2分子配分函数的计算

利用Gaussian03程序包,在B3P86/cc-PV5Z水平上对自由基SiH_2分子基态X~1A_1几何结构进行优化计算,得到其平衡几何结构、谐振频率和转动常数等性质参数;采用乘积近似法计算了自由基SiH_2分子基态X~1A_1从低温20 K到高温6000 K温度范围内的总配分函数.其中,转动配分函数采用WATSON的刚性转子模型,振动配分函数采用谐振子近似.然后我们把20～6000 K的温度范围划分为五个区间段,计算的总配分函数在这五个温度区间分别被拟合到一个温度T的四阶多项式,从而在每个区间均得到五个拟合系数.由这些拟合系数就可以快速、准确的获得该分子在所研究温度范围内任意温度的总的配分函数.     

Global weak solutions to Landau-Lifshitz equations into compact Lie algebras

We consider a parabolic system from a bounded domain in a Euclidean space or a closed Riemannian manifold into a unit sphere in a compact Lie algebra g; which can be viewed as the extension of Landau-Lifshitz (LL) equation and was proposed by V. Arnold. We follow the ideas taken from the work by the second author to show the existence of global weak solutions to the Cauchy problems of such LL equations from an n-dimensional closed Riemannian manifold T or a bounded domain in {ℝ}^n into a unit sphere {{\displaystyle S}}_g(\mathrm{1}) in g. In particular, we consider the Hamiltonian system associated with the nonlocal energy-micromagnetic energy defined on a bounded domain of {ℝ}^{\mathrm{3}} and show the initial-boundary value problem to such LL equation without damping terms admits a global weak solution. The key ingredient of this article consists of the choices of test functions and approximate equations.     

Construction of Coarse-Grained Models by Reproducing Equilibrium Probability Density Function

The present work proposes a novel methodology for constructing coarse-grained(CG) models, which aims at minimizing the difference between CG model and the corresponding original system. The difference is defined as a functional of their equilibrium conformational probability densities, then is estimated from equilibrium averages of many independent physical quantities denoted as basis functions. An orthonormalization strategy is adopted to get the independent basis functions from sufficiently preselected interesting physical quantities of the system. Thus the current method is named as probability density matching coarse-graining(PMCG) scheme, which effectively takes into account the overall characteristics of the original systems to construct CG model, and it is a natural improvement of the usual CG scheme wherein some physical quantities are intuitively chosen without considering their correlations. We verify the general PMCG framework in constructing a one-site CG water model from TIP3 P model. Both structure of liquids and pressure of the TIP3 P water system are found to be well reproduced at the same time in the constructed CG model.     

Deformation of thin straight pipes under concentrated forces or prescribed edge displacements

The purpose of this paper is to present an efficient analytic method for obtaining the deformation of thin straight pipes, subjected to prescribed edge displacements or concentrated loads.The approach uses the mixed formulation where unknown functions are combined with trigonometric terms. A variational procedure is used to obtain the system of ordinary differential equations. For the applied load a Fourier approach is used to represent the load as an analytical function. For the prescribed displacement, three solutions for the ovalization are evaluated and a method based on energy contribution of each term is used to obtain their superposition.In contrast to finite element method the proposed method is efficient and can be applied to other boundary condition problems leading to continuous displacement and stress fields with a low number of unknowns. Comparisons with experimental and finite element procedures show good agreement that enhances the merits of the analytical solutions proposed.The value of this method is based on solving the differential equations rather than using commercial codes. So far, the solution of prescribed edge displacements has been limited to one term. This paper discusses how to add further terms using the mixed formulation, thus, presenting a novel procedure.     

Analytical solutions of weakly coupled map lattices using recurrence relations

By using asymptotic methods recurrence relations are found that rule weakly CML evolution, with both global and diffusive coupling. The solutions obtained from these relations are very general because they do not hold restrictions about boundary conditions, initial conditions and number of oscilators in the CML. Furthermore, oscillators are ruled by an arbitraty C² function.