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Dumbbell Model for Dilute and Semi-Dilute Solutions
Dumbbell models are very crude representations of polymer molecules. Too crude to be of much interest to a polymer chemist, since it in no way...
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Equilibrium Statistics: Monte Carlo Methods
Monte Carlo methods use random numbers, or ‘random’ sequences, to sample from a known shape of a distribution, or to extract distribution by other...
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Computer Simulations of the Electric Double Layer
We describe the Lekner–Sperb summation technique used to calculate the Coulomb interaction in 2D periodic systems, and discuss in detail the methods...
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Molecular Dynamics of Complex Systems: Non-Hamiltonian, Constrained, Quantum-Classical
A theoretically sound and computationally tractable treatment for non-Hamiltonian molecular dynamics is needed for simulations of complex systems....
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Reverse Non-equilibrium Molecular Dynamics
We review non-equilibrium methods for calculating transport coefficients with emphasis on the reverse non-equilibrium molecular dynamics (RNEMD)...
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On the Reduction of Molecular Degrees of Freedom in Computer Simulations
Molecular simulations, based on atomistic force fields are a standard theoretical tool in materials, polymers and biosciences. While various methods,...
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Lattice Boltzmann Modeling of Complex Fluids: Colloidal Suspensions and Fluid Mixtures
The study of complex fluid dynamics requires development of numerical tools that capture the essentials of the dynamic coupling among the different...
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Mesoscopic Multi-particle Collision Model for Fluid Flow and Molecular Dynamics
Several aspects of modeling dynamics at the mesoscale level are discussed: (1) The construction of a mesoscopic description of fluid dynamics. The...
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6 Stepwise Inflation of a Balloon
When we inflate a balloon in the usual manner, namely by blowing air into it by mouth, we first inhale deeply by expanding our lungs. After that we...
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9 Stability of the Spherical Shape
Ever so often we observe that a balloon, which is spherical in the undistorted state, becomes elongated upon inflation so that we obtain a...
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Nonequilibrium Dynamics of Anisotropic Fluids
In Chap. 9 we summarized methods for analyzing the equilibrium statistics of physical system, using Monte Carlo methods. While at equilibrium complex...
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Connection between Different Levels of Description
One of the major issues raised by the Boltzmann equation is the problem of the reduced description. Equations of hydrodynamics constitute a closet...
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Irreducible and Isotropic Cartesian Tensors
In this chapter we summarize definitions and properties of cartesian, anisotropic, irreducible and isotropic tensors and related tensor operators. In...
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Chain Model for Dilute Solutions
Various experimental observations reveal an important aspect of the behavior of polymer solutions which is not captured by FENE dumbbell models. When...
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Chain Models for Transient and Semiflexible Structures
In order to be prepared for the analysis of the flexible FENE-C (FENE model which allows for scission/recombination), FENE-B (which allows for...
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Simulating the Dynamics of Mesoscopic Systems
We consider how to simulate quantitatively the dynamics of mesoscopic systems on macroscopic time-scales. In this respect we consider two relatively...
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Hybrid Models: Bridging Particle and Continuum Scales in Hydrodynamic Flow Simulations
Different models for the coupling of field and particle descriptions are introduced and examined. For the purpose of establishing how a molecular...
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1 Stability of Two Rubber Balloons
Rubber balloons, that usually adorn children’s parties, can also enchant the scientist. Indeed, there is much more than fun and games to be had with...
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2 Kinetic Theory of Rubber
We start by considering an elastic bar of any solid material, be it steel, aluminium, wood - or rubber. The bar is fixed to the bottom at one end and...