A New “Bounce-Normal” Boundary in DPD Calculations for the Reduction of Density Fluctuations

2008 ◽  
Author(s):  
Emadaldin Moeendarbary ◽  
K. Y. Lam ◽  
T. Y. Ng
Keyword(s):  
Shear Stress ◽  
Protein Separation ◽  
Dissipative Particle Dynamics ◽  
Computational Cost ◽  
Colloidal Suspensions ◽  
Density Fluctuations ◽  
Polymer Chains ◽  
New Method ◽  
Mems Devices ◽  
Macroscopic Properties

Dissipative Particle Dynamics (DPD) is a mesoscopic fluid modeling method, which facilitates the simulation of the statics and dynamics of complex fluid systems at physically interesting length and time scales. Currently, there are various applications of DPD, such as colloidal suspensions, multi-phase flow, rheology of polymer chains, DNA macromolecular suspension, etc., which employ this technique for their numerical simulation. The DPD technique is capable of modeling macroscopic properties of the bulk flow very well, but difficulties arise if the flows are confined through wall-bounded regions, or when different boundaries simultaneously exist in the simulation domain. These boundaries cause negative effects on the macroscopic temperature, density and velocity profiles, as well as the shear stress and pressure distributions. In particular, the interaction of DPD particles with solid boundaries causes large density fluctuations at the near wall regions. This density distortion leads to pronounced fluctuations in the pressure and shear stress, which are not actually present. To overcome these serious deficiencies, we introduce a new method in this work, which uses a combination of randomly distributed wall particles and a novel reflection adaptation at the wall. This new methodology is simple to implement and incurs no additional computational cost. More importantly, it does not cause any distortion in the macroscopic properties. This novel reflection adaptation is a novel version of the bounce back reflection, which we shall term the bounce-normal reflection. The most important characteristic of this method is that it reduces density fluctuations near the boundaries without affecting the velocity and temperature profiles. This new method is easily applicable to any wall-bounded problem with stationary boundaries and it has a very good consistency with macroscopic features. The eventual objective of this numerical development work is to investigate suspension flow through micro/nano channels of fluidic NEMS/MEMS devices, with applications to DNA and protein separation. These micro/nano channel devices, consisting of many entropic traps, are designed and fabricated for the separation of proteins and long DNA molecules.

scholarly journals Renormalization group theory of molecular dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Daiji Ichishima ◽  
Yuya Matsumura
Keyword(s):  
Molecular Dynamics ◽  
Renormalization Group ◽  
Critical Exponent ◽  
Computational Efficiency ◽  
Large Scale ◽  
Dissipative Particle Dynamics ◽  
Computational Cost ◽  
Coarse Graining ◽  
Spatial Dimension ◽  
Deborah Number

AbstractLarge scale computation by molecular dynamics (MD) method is often challenging or even impractical due to its computational cost, in spite of its wide applications in a variety of fields. Although the recent advancement in parallel computing and introduction of coarse-graining methods have enabled large scale calculations, macroscopic analyses are still not realizable. Here, we present renormalized molecular dynamics (RMD), a renormalization group of MD in thermal equilibrium derived by using the Migdal–Kadanoff approximation. The RMD method improves the computational efficiency drastically while retaining the advantage of MD. The computational efficiency is improved by a factor of $$2^{n(D+1)}$$ 2 n ( D + 1 ) over conventional MD where D is the spatial dimension and n is the number of applied renormalization transforms. We verify RMD by conducting two simulations; melting of an aluminum slab and collision of aluminum spheres. Both problems show that the expectation values of physical quantities are in good agreement after the renormalization, whereas the consumption time is reduced as expected. To observe behavior of RMD near the critical point, the critical exponent of the Lennard-Jones potential is extracted by calculating specific heat on the mesoscale. The critical exponent is obtained as $$\nu =0.63\pm 0.01$$ ν = 0.63 ± 0.01 . In addition, the renormalization group of dissipative particle dynamics (DPD) is derived. Renormalized DPD is equivalent to RMD in isothermal systems under the condition such that Deborah number $$De\ll 1$$ D e ≪ 1 .

An explicit method to calculate implicit spatial finite differences

Geophysics ◽  
2021 ◽  
pp. 1-71
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Computational Cost ◽  
New Method ◽  
Seismic Exploration ◽  
Explicit Method ◽  
Lu Decomposition ◽  
Implicit Methods ◽  
Band Matrices ◽  
Explicit Finite Difference

The finite-difference solution of the second-order acoustic wave equation is a fundamental algorithm in seismic exploration for seismic forward modeling, imaging, and inversion. Unlike the standard explicit finite difference (EFD) methods that usually suffer from the so-called "saturation effect", the implicit FD methods can obtain much higher accuracy with relatively short operator length. Unfortunately, these implicit methods are not widely used because band matrices need to be solved implicitly, which is not suitable for most high-performance computer architectures. We introduce an explicit method to overcome this limitation by applying explicit causal and anti-causal integrations. We can prove that the explicit solution is equivalent to the traditional implicit LU decomposition method in analytical and numerical ways. In addition, we also compare the accuracy of the new methods with the traditional EFD methods up to 32nd order, and numerical results indicate that the new method is more accurate. In terms of the computational cost, the newly proposed method is standard 8th order EFD plus two causal and anti-causal integrations, which can be applied recursively, and no extra memory is needed. In summary, compared to the standard EFD methods, the new method has a spectral-like accuracy; compared to the traditional LU-decomposition implicit methods, the new method is explicit. It is more suitable for high-performance computing without losing any accuracy.

scholarly journals EFFICIENT LINE DETECTION METHOD BASED ON 2D CONVOLUTION FILTER

2021 ◽  
Vol 11 (4) ◽  
pp. 22-27
Author(s):  
Paweł Kowalski ◽  
Piotr Tojza
Keyword(s):  
Detection Method ◽  
Computational Cost ◽  
New Method ◽  
Line Detection ◽  
Curve Detection ◽  
Real Time Image ◽  
Convolution Filter ◽  
Straight Lines ◽  
Time Image ◽  
Local Detection

The article proposes an efficient line detection method using a 2D convolution filter. The proposed method was compared with the Hough transform, the most popular method of straight lines detection. The developed method is suitable for local detection of straight lines with a slope from -45˚ to 45˚.  Also, it can be used for curve detection which shape is approximated with the short straight sections. The new method is characterized by a constant computational cost regardless of the number of set pixels. The convolution is performed using the logical conjunction and sum operations. Moreover, design of the developed filter and the method of filtration allows for parallelization. Due to constant computation cost, the new method is suitable for implementation in the hardware structure of real-time image processing systems.

scholarly journals A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations

2021 ◽  
Author(s):  
Tobias Leibner ◽  
Mario Ohlberger
Keyword(s):  
Optimization Problems ◽  
Hessian Matrix ◽  
Computational Cost ◽  
Kinetic Equations ◽  
New Method ◽  
Minimum Entropy ◽  
Reduced Basis ◽  
Simple Task ◽  
Wide Range ◽  
The Moment

In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic equations that conserve many of the fundamental physical properties of solutions. However, their practical use is limited by their high computational cost, as an optimization problem has to be solved for every cell in the space-time grid. In addition, implementation of numerical solvers for these models is hampered by the fact that the optimization problems are only well-defined if the moment vectors stay within the realizable set. For the same reason, further reducing these models by, e.g., reduced-basis methods is not a simple task. Our new method overcomes these disadvantages of classical approaches. The transformation is performed on the semi-discretized level which makes them applicable to a wide range of kinetic schemes and replaces the nonlinear optimization problems by inversion of the positive-definite Hessian matrix. As a result, the new scheme gets rid of the realizability-related problems. Moreover, a discrete entropy law can be enforced by modifying the time stepping scheme. Our numerical experiments demonstrate that our new method is often several times faster than the standard optimization-based scheme.

A new method for human milk protein separation

Biochimie ◽  
1982 ◽  
Vol 64 (3) ◽  
pp. 231-235 ◽  
Author(s):  
Ghislaine Brignon ◽  
Bruno Ribadeau-Dumas
Keyword(s):  
Human Milk ◽  
Protein Separation ◽  
Milk Protein ◽  
New Method ◽  
Human Milk Protein
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