We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions;thes...
详细信息
We present efficient algorithms to calculate trajectories for periodic Lorentz gases consisting of square lattices of circular obstacles in two dimensions, and simple cubic lattices of spheres in three dimensions;these become increasingly efficient as the radius of the obstacles tends to 0, the so-called Boltzmann-Grad limit. The 2D algorithm applies continued fractions to obtain the exact disc with which a particle will collide at each step, instead of using periodic boundary conditions as in the classical algorithm. The 3D version incorporates the 2D algorithm by projecting to the three coordinate planes. As an application, we calculate distributions of free path lengths close to the Boltzmann-Grad limit for certain Lorentz gases. We also show how the algorithms may be applied to deal with general crystal lattices.
We introduce an algorithm for the explicit treatment of contact line motion for thin- film problems and compare its solutions with exact source-type solutions and their asymptotic behavior near the contact line. The a...
详细信息
We introduce an algorithm for the explicit treatment of contact line motion for thin- film problems and compare its solutions with exact source-type solutions and their asymptotic behavior near the contact line. The algorithm uses a variational formulation and avoids dealing with singularities near the contact line.
An explicit procedure is given to construct exact closed‐form solutions to the time‐independent Schr?dinger equation in two dimensions [?2+λ?w(x,y)]ψ=0, where w(x,y) is a polynomial potential of degree greater tha...
详细信息
An explicit procedure is given to construct exact closed‐form solutions to the time‐independent Schr?dinger equation in two dimensions [?2+λ?w(x,y)]ψ=0, where w(x,y) is a polynomial potential of degree greater than two not separable in Cartesian coordinates. Several examples are discussed for which w(x,y) is a sextic polynomial. As has already been seen in studies of the corresponding one‐dimensional problem, a complete set of eigenvalues and wave functions is not found. However, these closed‐form solutions can be used to check the accuracy and efficiency of numerical algorithms.
A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman-Ziff algorithm. T...
详细信息
A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman-Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman-Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.
In this paper a new anisotropic silicon etching model is proposed. The crystalline planes propagation model consists in the decomposition of the polygonal contour over a finite basis of planes, insertion of the emerge...
详细信息
In this paper a new anisotropic silicon etching model is proposed. The crystalline planes propagation model consists in the decomposition of the polygonal contour over a finite basis of planes, insertion of the emergent planes, the displacement of all planes over the normal direction, elimination of non-physical ones and generation of the etched contour. Also, the paper presents examples of application and experimental tests. The method demonstrates an accurate simulation of the reality. Furthermore, it is easy to implement and adapt to other materials.
Some theoretical aspects of surface topography evolution during ion beamerosion are discussed. In particular, the theory of characteristics is considered in some detail and its limitations pointed out. Further theoret...
详细信息
Some theoretical aspects of surface topography evolution during ion beamerosion are discussed. In particular, the theory of characteristics is considered in some detail and its limitations pointed out. Further theoretical development based on the Huygens principle of wave propagation is discussed also with respect to numerical evaluation of surface evolution. A new numerical algorithm based on the contemporary theoretical concepts of surface and edge propagation is proposed and compared with existing numerical models and theoretical expectations.
A fundamentally new method for determining the eigenvalues of linear differential operators is presented. The method involves the application of moment analysis and affords a fast and precise numerical algorithm for e...
详细信息
A fundamentally new method for determining the eigenvalues of linear differential operators is presented. The method involves the application of moment analysis and affords a fast and precise numerical algorithm for eigenvalue computation, particularly in the intermediate and strong coupling regimes. The most remarkable feature of this approach is that it provides exponentially converging lower and upper bounds to the eigenvalues. The effectiveness of this method is demonstrated by applying it to an important magnetohydrodynamics problem recently studied by Paris, Auby, and Dagazian [J. Math. Phys. 2 7, 2188 (1986)]. Through the very precise lower and upper bounds obtained, this approach gives full support to their analysis.
The aim of the paper is to present a method for the design of a glide-slope coupler of an aircraft using an optimal H ∞ approach obtained via the theory of singularly perturbed systems. The benefits of this optimal d...
详细信息
The aim of the paper is to present a method for the design of a glide-slope coupler of an aircraft using an optimal H ∞ approach obtained via the theory of singularly perturbed systems. The benefits of this optimal design procedure are emphasized by comparing computational aspects, tracking and robustness performances with the ones obtained when using suboptimal H ∞ methods.
For arbitrary precision numbers, reciprocal computing algorithms based on Newton iteration is asymptotically the fastest. In this work we provide a refined a lgorithm based on the Newton reciprocal algorithm by Brent ...
详细信息
For arbitrary precision numbers, reciprocal computing algorithms based on Newton iteration is asymptotically the fastest. In this work we provide a refined a lgorithm based on the Newton reciprocal algorithm by Brent and Zimmermann in their MCA book. The key techniques used in the refinement are D1 balancing, clear specification, r emainder o peration, and economical multiplication. The refined algorithm is more general,and gives exact and unique result. numerical results show that these improvements are made without the cost of time *** is still the potential to further improve the efficiency by utilizing a short multiplication algorithm.
Langevin dynamics is a typical thermostat for canonical MD simulations. Various schemes may be proposed for numerical integration of the Langevin equation. Accuracy and efficiency of the simulation strongly replies on...
详细信息
Langevin dynamics is a typical thermostat for canonical MD simulations. Various schemes may be proposed for numerical integration of the Langevin equation. Accuracy and efficiency of the simulation strongly replies on the numerical algorithm employed to solve the Langevin equation. In this article, we study twelve useful schemes for Langevin dynamics. For both the stationary state distribution and the characteristic correlation time of the one-dimensional harmonic system, we introduce two approaches to investigate the twelve schemes. They include a direct approach that is based on the trajectory of Langevin dynamics, and an indirect approach that employs the mean value and the phase space propagator. All the schemes are employed in the MD simulations of two model systems(harmonic potential and quartic potential).
暂无评论