Tree Particle‐Mesh: An Adaptive, Efficient, and Parallel Code for Collisionless Cosmological Simulation

We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics—the Langevin/implicit-Euler scheme—is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω≫ωc, where ωc is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme—frictional and intrinsic—and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces ‘‘correct’’ transition rates for a model potential whose energy distribution is ‘‘well-described’’ classically.

Two algorithms are presented for integrating the Langevin dynamics equation with long numerical time steps while treating the mass terms as finite. The development of these methods is motivated by the need for accurate methods for simulating slow processes in polymer systems such as two-site intermolecular distances in supercoiled DNA, which evolve over the time scale of milliseconds. Our new approaches refine the common Brownian dynamics (BD) scheme, which approximates the Langevin equation in the highly damped diffusive limit. Our LTID (“long-time-step inertial dynamics”) method is based on an eigenmode decomposition of the friction tensor. The less costly integrator IBD (“inertial Brownian dynamics”) modifies the usual BD algorithm by the addition of a mass-dependent correction term. To validate the methods, we evaluate the accuracy of LTID and IBD and compare their behavior to that of BD for the simple example of a harmonic oscillator. We find that the LTID method produces the expected correlation structure for Langevin dynamics regardless of the level of damping. In fact, LTID is the only consistent method among the three, with error vanishing as the time step approaches zero. In contrast, BD is accurate only for highly overdamped systems. For cases of moderate overdamping, and for the appropriate choice of time step, IBD is significantly more accurate than BD. IBD is also less computationally expensive than LTID (though both are the same order of complexity as BD), and thus can be applied to simulate systems of size and time scale ranges previously accessible to only the usual BD approach. Such simulations are discussed in our companion paper, for long DNA molecules modeled as wormlike chains.

Osborne et al [Phys. Rev. E 74, 036309 (2006)] suggested that our conclusions on the ability of kinematic simulation to represent the t(3) Richardson law [Thomson and Devenish, J. Fluid Mech. 526, 277 (2005)] were an artifact of our choice of time step. Here we repeat some of the simulations with a small fixed time step, enabling us to confirm that our previous study was not compromised by the variable time step used.

The design of the channel part of a digital communication system (e.g., error correction, modulation) is heavily based on the assumption that the data to be transmitted forms a fair bit stream. However, simple source encoders such as short Huffman codes generate bit streams that poorly match this assumption. As a result, the channel input distribution does not match the original design criteria. In this work, a simple method called half Huffman coding (HALFHC) is developed. HALFHC transforms a Huffman code into a source code whose output is more similar to a fair bit stream. This is achieved by permuting the codewords such that the frequency of 1s at the output is close to 0.5. The permutations are such that the optimality in terms of achieved compression ratio is preserved. HALFHC is applied in a practical example, and the resulting overall system performs better than when conventional Huffman coding is used.

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

A tree coding theorem is established for discrete-time abstract alphabet stationary block-ergodic sources under a single-letter fidelity criterion. The proof of this theorem uses recent results from the theory of branching processes with random environments. The relation to previous work in tree coding is also discussed.

A space-efficient Huffman decoding algorithm and its parallelism

Simulation errors due to insufficient temporal rainfall resolution — Annual combined sewer overflow

A computationally efficient forest succession model: Design and initial tests

Representation of the canopy hydrological processes has been challenging in land surface modeling due to the subgrid heterogeneity in both precipitation and surface characteristics. The Shuttleworth dynamic–statistical method is widely used to represent the impact of the precipitation subgrid variability on canopy hydrological processes but shows unwanted sensitivity to temporal resolution when implemented into land surface models. This paper presents a canopy hydrology scheme that is robust at different temporal resolutions. This scheme is devised by applying two physically based treatments to the Shuttleworth scheme: 1) the canopy hydrological processes within the rain-covered area are treated separately from those within the nonrain area, and the scheme tracks the relative rain location between adjacent time steps; and 2) within the rain-covered area, the canopy interception is so determined as to sustain the potential evaporation from the wetted canopy or is equal to precipitation, whichever is less, to maintain somewhat wet canopy during any rainy time step. When applied to the Amazon region, the new scheme establishes interception loss ratios of 0.3 at a 10-min time step and 0.23 at a 2-h time step. Compared to interception loss ratios of 0.45 and 0.09 at the corresponding time steps established by the original Shuttleworth scheme, the new scheme is much more stable under different temporal resolutions.

In this contribution we present an extension of the multiscale Capriccio method towards inelasticity. This enables coupled simulations of a particle domain embedded into a continuum with particular focus on polymer systems. Starting from the method's initial implementation of pure elasticity, we substitute the nonlinear elastic continuum constitutive law by a recently developed viscoelastic‐viscoplastic one which is able to capture the mechanical behaviour of the particle system in a much larger strain range. Furthermore, we discuss numerical aspects like the choice of time steps and iteration numbers.

The application of computers to circuit design is discussed, with particular emphasis on the analysis of nonlinear circuits in the time domain. Circuit modelling and numerical integration are considered in detail. It is concluded that it is better to use only basic elements and to build up more complicated devices (e.g. transistors) from these. The most suitable integration formula is the trapezoidal rule, provided that a suitable method of time-step adjustment is used. The choice of time step may be based on the estimation of the local truncation error, or on a comparison of the results computed with different step lengths. For nonlinear circuits, the latter method has been found to be superior. A computer program, TRAN, based on these conclusions, has been written in ASA FORTRAN. It is suitable for use on a time-sharing system or a minicomputer, and has been used on a wide range of problems. Several examples of its use are given.

Selective encryption only encrypts a portion of a compressed bitstream, relying on the characteristics of the compression format to render the remaining in-the-clear content unusable. While the technique has been proposed in a number of practical applications, it is also motivated by concepts from the origins of Shannon theory on the links between source coding and encryption and benefits from an evaluation of its performance on compression primitives, such as quantization and Huffman coding, used in constructing many compression algorithms.

We present adaptive on-line schemes for lossy encoding of individual sequences, under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this paper, a set of fixed-rate scalar source codes with zero delay is presented. We propose a randomized on-line coding scheme, which achieves asymptotically (and with high probability), the performance of the best source code in the set, uniformly over all source sequences. Efficient algorithms for implementing this scheme for small and large sets of encoders are presented. In the second part of this work, we generalize our results to the case of variable-rate coding. A set of variable-rate scalar source codes is presented. This time, the performance is measured by the Lagrangian Cost (LC), which is defined as a weighted sum of the distortion and the length of the encoded sequence. Efficient algorithms for implementing the generalized on-line coding scheme are presented. We then consider the special case of lossless variable-rate coding. An on-line scheme which uses Huffman codes is presented. We show that this scheme can be implemented efficiently using the same graphic methods from the first part. Finally, combining the results from former sections, we build a generalized efficient algorithm for a structured set of variable-rate encoders.

Through information theory, problems of communication and compression can be precisely modeled, formulated, and analyzed, and this information can be transformed by means of algorithms. Also, learning can be viewed as compression with side information. Aimed at students and researchers, this book addresses data compression and redundancy within existing methods and central topics in theoretical data compression, demonstrating how to use tools from analytic combinatorics to discover and analyze precise behavior of source codes. It shows that to present better learnable or extractable information in its shortest description, one must understand what the information is, and then algorithmically extract it in its most compact form via an efficient compression algorithm. Part I covers fixed-to-variable codes such as Shannon and Huffman codes, variable-to-fixed codes such as Tunstall and Khodak codes, and variable-to-variable Khodak codes for known sources. Part II discusses universal source coding for memoryless, Markov, and renewal sources.