Small Step Size Research Articles

Simulation of red blood cell motion in microvessels using modified moving particle semi-implicit method

Red Blood Cells (RBCs) are the main cells in human blood, with a main role in the mechanical properties of blood as a fluid. Several methods have been improved to simulate the mechanical behavior of RBC in micro-capillaries. Since, in microscopic scales, using discrete models is more preferred than continuum methods, the Moving Particle Semi-Implicit method (MPS), which is a recent innovative particle based method, can simulate micro-fluidic flows based on Navier–Stokes equations. Although, by recent developments, the MPS method has turned into a considerable tool for modeling blood flow in micro meter dimensions, some problems, such as a commitment to use small time step sizes, still restrict the method for large models and also for long time simulations. A new modified semi-implicit algorithm is developed and implemented on RBC motion through microvessels, in order to reduce calculation time by more than a factor of twenty, while the error of position and velocity remains constant. A two-dimensional, parallel plate, fluid flow is simulated based on the proposed method, and the effect of the calculation time decrement is evaluated. Findings indicate a reduction of 90 percent in simulation time compared to previous studies with the same results. This significant developed method could be applied to RBC interaction within micro-capillaries and constricted zones in blood flow.

Streamline based black-oil simulation and its application to waterflooding

Finite-difference method is widely used for solving large-scale multiphase displacement problems. Drawbacks of finite difference methods are numerical dispersion, grid orientation, small time step size, and large computation time. To overcome these problems, streamline methods are being developed in which fluid is transported along the streamlines instead of the finite difference grid. This paper describes the development and application of a three-dimensional black-oil streamline simulator to study water flooding in a quarter five spot pattern. Larger time steps and higher spatial resolution can be achieved in these simulations. Streamline simulator is benchmarked against finite difference simulator (UTCOMP) for different test cases. Predictions from streamline simulator are in good agreement with the results from finite difference simulation, however speed up factor of up to 12 times is observed with streamline simulator. Results from the streamline simulator are also compared with the laboratory scale experimental data which shows a fairly good match. The 3-D streamline simulator is further extended to study the impact of various factors on the water flood performance.

740 拘束条件式を近似したマルチボディ車両モデルのリアルタイム解析

In this paper, the performance of the real-time multibody dynamic simulation with linearized constraint equation is discussed. It is well known that a small step size of numerical integration is required for the simulation of a system with high stiffness elements such as a rubber bush or a system with high frequency phenomena. The amount of the calculation can be reduced by linearizing the constraint equation of the system, and a real-time multibody dynamic analysis with smaller step size of numerical integration can be realized. On the other hand, it is important to understand how much accuracy was lost by the linearization. In this study, we compared the real-time simulation result with the linearized and the non-linearized multibody model in the case of the vehicle dynamic simulation. The calculation speed was evaluated on a real-time analysis environment, and the accuracy of the simulation result was examined.

Improving the Reliability of EBSD-Based Texture Analysis by a New Large Area Mapping Technique

The relevance of EBSD-based investigations for statements on the macroscopic or mesoscopic behavior of materials is critically relying on the statistical representativeness of the data. Particularly, the statistical reliability of the EBSD-based results (e.g. texture, phase fraction or grain size) remains an open question since the areas observed by the EBSD technique are quite small compared to XRD techniques. It has already been shown that covering larger areas and probing more grains with the help of large step sizes is beneficial in terms of representativeness [1]. On the other hand, small step sizes are beneficial in terms of grain reconstruction and data clean-up. However, step sizes significantly smaller than the average grain size of the material lead to either covered areas or number of probed grains being too small to be representative or to very large datasets and correspondingly long measurement times. In this contribution, the benefits of a new mapping technique [1] that joins the advantages of large and small step size measurements will be demonstrated. The representativeness of the EBSD datasets obtained by classical and this new mapping techniques were compared by calculating the pole figure symmetries of a TRIP steel. The results show that the proposed mapping technique significantly improves the reliability and representativeness of EBSD-based texture measurements.

Fully implicit time discretization for a free surface flow problem

AbstractOne of the challenges in the numerics of free surface flows is the coupling of the flow field to the geometry of the domain. The most simple approach is an explicit decoupling, i.e. computing the flow field with geometrical information of a prior time step and then updating the geometry. This widely used approach leads to a severe CFL condition of the type $\Delta t \le C\sqrt{{\rm We}}\;h^{3 \over 2}$, which may prescribe infinitesimally small time step sizes in the interesting case of a small Weber number (i.e. high surface tension). A semi‐implicit approach utilizing the fact that $x^{n+1} = x^n + \Delta t\, u^{n+1}_{|\Gamma}$, where xk is a parametrization of the capillary boundary Γ, is also available [1]. This approach can be proven to be unconditionally stable but is of first order only. It also suffers from relatively strong numerical dissipation.We present a fully implicit approach using a backward differentiation formula to achieve a time discretization method that is of second order and only minimally dissipative. A numerical example of an oscillating drop showing very low numerical dissipation and second order convergence as well as numerical evidence for the stability of the method is presented. Since the method requires the solution of a highly nonlinear coupled system, possible preconditioners for this system are discussed, including a lower order decoupling. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Parameter Estimation of the Extended Vasiček Model

In this paper, an estimate of the drift and diffusion parameters of the extended Vasicek model is presented. The estimate is based on the method of maximum likelihood. We derive a closed-form expansion for the transition (probability) density of the extended Vasicek process and use the expansion to construct an approximate log-likelihood function of a discretely sampled data of the process. Approximate maximum likelihood estimators (AMLEs) of the parameters are obtained by maximizing the approximate log-likelihood function. The convergence of the AMLEs to the true maximum likelihood estimators is obtained by increasing the number of terms in the expansions with a small time step size.

DC Coefficient Distributions for P-Frames in H.264/AVC

In this letter, the distributions of direct current (DC) coefficients for P-frames in H.264/AVC are analyzed, and the distortion model of the Gaussian source under the quantization of the dead-zone plus-uniform threshold quantization with uniform reconstruction quantizer is derived. Experimental results show that the DC coefficients of P-frames are best approximated by the Laplacian distribution and the Gaussian distribution at small quantization step sizes and at large quantization step sizes, respectively.

Design of C-Band Wideband Sweep Frequency Source

This paper presents the design and fabrication of a compact 4-8GHz sweep frequency source at C-band with a hybrid frequency synthesizer technology. With DDS used as PLL’s reference, the frequency step size is as small as 3×10-4 Hz and the measured 1 kHz offset phase noise is-91.79dBc/Hz at 4GHz. This frequency sweep source has advantages of wide bandwidth, low phase noise, small frequency step size, low spurious, fast tuning speed, small size and low power consumption. So it is suitable for wireless hand-held test equipment and communication equipment.

Geometric integration of Hamiltonian systems perturbed by Rayleigh damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter ε, and the schemes under study preserve the symplectic structure in the case ε=0. In the case 0<ε≪1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order.

Convergence and stability of the balanced methods for stochastic differential equations with jumps

This paper deals with the balanced methods which are implicit methods for stochastic differential equations with Poisson-driven jumps. It is shown that the balanced methods give a strong convergence rate of at least 1/2 and can preserve the linear mean-square stability with the sufficiently small stepsize. Weak variants are also considered and their mean-square stability analysed. Some numerical experiments are given to demonstrate the conclusions.

Generalized power series method with step size control for neutron kinetics equations

Based on the power series method (PWS), a generalized power series method (GPWS) has been introduced for solving the point reactor kinetics equations. The stiffness of the kinetics equations restricts the time interval to a small increment, which in turn restricts the PWS method within a very small constant step size. The traditional PWS method has been developed using a new formula that can control the time step at each step while transient proceeds. Two solvers of the PWS method using two successive orders have been used to estimate the local truncation errors. The GPWS method has employed these errors and some other constraints to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The proposed method has resolved the stiffness point kinetics equations in a very simple way with step, ramp and zigzag ramp reactivities. The generalized method has turned out to represent a fast and accurate computational technique for most applications. The method is seemed to be valid for a time interval that is much longer than the time interval used in the conventional numerical integration, and is thus useful in reducing computing time. The method constitutes an easy-to-implement algorithm that provides results with high accuracy for most applications where, the reactor kinetics equations are reduced to a differential equation in a matrix form convenient for explicit power series solution. Results obtained by GPWS method: attest the power of the theoretical analysis, they demonstrate that the convergence of the iteration scheme can be accelerated, and the resulting computing time can be greatly reduced while maintaining computational accuracy. The point kinetics equations have been solved as a preliminary simple case aimed at testing the applicability of the GPWS method to solve point kinetics equations with feedback or, space kinetics problems.

P‐81: Thin Beam Laser Crystallization Technology in AMOLED and AMLCD Applications

AbstractThin beam laser crystallization technology is presented. It has the features of long beam length &gt;730mm, controllable thin beam width 3∼22um and high laser frequency 3000∼6000Hz. Due to the features, it can process display transistor backplane with small laser step size 1∼4um while keeping high production throughput. The effect of small laser step size related to poly‐crystalline silicon transistor uniformity is investigated here. The transistor channel of the display backplane can cross multiple step size areas that result in an averaging effect of the laser pulses and obtain uniform transistor characteristics.

Force Generation: ATP-Powered Proteasomes Pull the Rope

Recently, single-molecule force spectroscopy techniques have provided unprecedented opportunities to apply and to quantify forces that guide protein (un-)folding. A new study provides fascinating insights into the sophisticated mechanism by which an ATP-fueled proteolytic machine generates mechanical forces to unfold and translocate multidomain substrates.

The RSC chromatin remodelling ATPase translocates DNA with high force and small step size

ATP-dependent chromatin remodelling complexes use the energy of ATP hydrolysis to reposition and reconfigure nucleosomes. Despite their diverse functions, all remodellers share highly conserved ATPase domains, many shown to translocate DNA. Understanding remodelling requires biophysical knowledge of the DNA translocation process: how the ATPase moves DNA and generates force, and how translocation and force generation are coupled on nucleosomes. Here, we characterize the real-time activity of a minimal RSC translocase 'motor' on bare DNA, using high-resolution optical tweezers and a 'tethered' translocase system. We observe on dsDNA a processivity of ∼35 bp, a speed of ∼25 bp/s, and a step size of 2.0 (±0.4, s.e.m.) bp. Surprisingly, the motor is capable of moving against high force, up to 30 pN, making it one of the most force-resistant motors known. We also provide evidence for DNA 'buckling' at initiation. These observations reveal the ATPase as a powerful DNA translocating motor capable of disrupting DNA-histone interactions by mechanical force.

Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits

We perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics, in which the mechanics sub-problem is solved first. We consider slow deformations, so that inertia is negligible and the mechanical problem is governed by an elliptic equation. We use Biot’s self-consistent theory to obtain the classical parabolic-type flow problem. We use a generalized midpoint rule (parameter α between 0 and 1) time discretization, and consider two classical sequential methods: the drained and undrained splits. The von Neumann method provides sharp stability estimates for the linear poroelasticity problem. The drained split with backward Euler time discretization ( α = 1) is conditionally stable, and its stability depends only on the coupling strength, and it is independent of time step size. The drained split with the midpoint rule ( α = 0.5) is unconditionally unstable. The mixed time discretization, with α = 1.0 for mechanics and α = 0.5 for flow, has the same stability properties as the backward Euler scheme. The von Neumann method indicates that the undrained split is unconditionally stable when α ⩾ 0.5. We extend the stability analysis to the nonlinear regime (poro-elastoplasticity) via the energy method. It is well known that the drained split does not inherit the contractivity property of the continuum problem, thereby precluding unconditional stability. For the undrained split we show that it is B-stable (therefore unconditionally stable at the algorithmic level) when α ⩾ 0.5. We also analyze convergence of the drained and undrained splits, and derive the a priori error estimates from matrix algebra and spectral analysis. We show that the drained split with a fixed number of iterations is not convergent even when it is stable. The undrained split with a fixed number of iterations is convergent for a compressible system (i.e., finite Biot modulus). For a nearly-incompressible system (i.e., very large Biot modulus), the undrained split loses first-order accuracy, and becomes non-convergent in time. We also study the rate of convergence of both splits when they are used in a fully-iterated sequential scheme. When the medium permeability is high or the time step size is large, which corresponds to a high diffusion of pressure, the error amplification of the drained split is lower and therefore converges faster than the undrained split. The situation is reversed in the case of low permeability and small time step size. We provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits, in the linear and nonlinear regimes. We also show that our spatial discretization (finite volumes for flow and finite elements for mechanics) removes the well-documented spurious instability in consolidation problems at early times.

RK-Slim: embedded Runge-Kutta without the excess baggage

Computationally demanding scientific simulations require numerical integration of large systems of ordinary differential equations (ODEs) in real time. Runge–Kutta (RK) methods with step-size control are frequently employed because they are accurate and have short execution times. Computational step sizes can be increased while maintaining accuracy if the error generated during each time step is below a predetermined threshold. However, if the error exceeds the threshold, the time step must be re-computed using a smaller step-size. In practice, the re-computation is unnecessary for most equations in the system because violations of the error tolerance are localized and occur in just a few equations. We present an efficient and accurate method for solving ODEs that exploits these observations on step-size by eliminating many unnecessary computations in embedded RK methods. We demonstrate how our new method can be a valuable tool for practitioners in the field through simulations with real-world data. Copyright © 2011 John Wiley & Sons, Ltd.

The RSC Chromatin Remodeling ATPase can Translocate DNA with High Force and Small Step Size

ATP-dependent chromatin remodeling complexes (remodelers) use the energy of ATP hydrolysis to reposition and reconfigure nucleosomes. Despite their diverse functions, all remodelers share highly conserved catalytic ATPase domains, many of which are shown to translocate DNA. Understanding remodeling requires biophysical knowledge of the DNA translocation process: how the ATPase moves DNA and generates force, and how translocation and force generation are coupled on nucleosomes. Here we characterize the real-time activity of a minimal translocase ‘motor’ complex isolated from a prototypical remodeler (RSC) on bare DNA, using high-resolution optical tweezers and a ‘tethered’ translocase system. We observe on dsDNA a processivity of ∼35 bp, a speed of ∼25 bp/sec, and a step size of 1.9 (± 0.3, s.d.) bp. Surprisingly, the motor is capable of moving against high force, up to 30 pN, making it one of the most force-resistant motors known. We also provide evidence for DNA ‘buckling’ at initiation. These observations extend and clarify measurements of nucleosome-dependent translocation by the complete RSC or SWI/SNF complex, and reveal the ATPase as a powerful and versatile DNA translocating motor capable of disrupting DNA-histone interactions by mechanical force using a small step size.

Output statistics of a line enhancer based on a combination of two adaptive filters

AbstractThis paper studies output statistics of an adaptive line enhancer that is based on an affine combination of two NLMS adaptive filters. Combination of adaptive filters is a new interesting way of improving the performance of adaptive algorithms. The structure consists of two adaptive filters that adapt on the same input signal, one with a large and the other one with a small step size. Such a combination is capable of achieving fast initial convergence and small steady state error at the same time. In this paper we investigate the second order statistics of the output signal of adaptive line enhancer based on the combination in steady state. The result is given in terms of the parameters of the adaptive combination, input process statistics, and the optimal Wiener filter weights for the problem at hands.

Step Sizes for Strong Stability Preservation with Downwind-Biased Operators

Strong stability preserving (SSP) integrators for initial value ODEs preserve temporal monotonicity solution properties in arbitrary norms. All existing SSP methods, including implicit methods, either require small step sizes or achieve only first order accuracy. It is possible to achieve more relaxed step size restrictions in the discretization of hyperbolic PDEs through the use of both upwind- and downwind-biased semidiscretizations. We investigate bounds on the maximum SSP step size for methods that include negative coefficients and downwind-biased semi-discretizations. We prove that the downwind SSP coefficient for linear multistep methods of order greater than one is at most equal to two, while the downwind SSP coefficient for explicit Runge–Kutta methods is at most equal to the number of stages of the method. In contrast, the maximal downwind SSP coefficient for second order Runge–Kutta methods is shown to be unbounded. We present a class of such methods with arbitrarily large SSP coefficient and demonstrate that they achieve second order accuracy for large CFL number.

Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations

By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately.