Search results for "Boundary value problem"
showing 10 items of 551 documents
Investigation of Finite-Size Effects in the Determination of Interfacial Tensions
2014
The interfacial tension between coexisting phases of a material is an important parameter in the description of many phenomena such as crystallization, and even today its accurate measurement remains difficult. We have studied logarithmic finite-size corrections in the determination of the interfacial tension with large scale Monte Carlo simulations, and have identified several novel contributions which not only depend on the ensemble, but also on the type of the applied boundary conditions. We present results for the Lennard-Jones system and the Ising model, as well as for hard spheres, which are particularly challenging. In the future, these findings will contribute to the understanding a…
Quantum Monte Carlo study of high pressure solid molecular hydrogen
2013
We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating…
ChemInform Abstract: Tuning the Defect Configurations in Nematic and Smectic Liquid Crystalline Shells
2013
Thin liquid crystalline shells surrounding and surrounded by aqueous phases can be conveniently produced using a nested capillary microfluidic system, as was first demonstrated by Fernandez-Nieves et al. in 2007. By choosing particular combinations of stabilizers in the internal and external phases, different types of alignment, uniform or hybrid, can be ensured within the shell. Here, we investigate shells in the nematic and smectic phases under varying boundary conditions, focusing in particular on textural transformations during phase transitions, on the interaction between topological defects in the director field and inclusions in the liquid crystal (LC), and on the possibility to relo…
Direct observation of a buckling transition during the formation of thin colloidal crystals
2007
We have investigated a colloidal suspension in a thin wedge formed by two glass plates in the presence of a lateral pressure. Starting with a single hexagonal layer, with increasing separation between the glass plates additional layers are added. This process is accompanied by a number of structural transitions necessary to maintain a high packing fraction under the given boundary conditions. Besides the well-known sequence of hexagonal and quadratic phases, we observe two new phases which are identified with the buckling and the rhombic phase recently predicted by other authors.
A New Colloid Model for Dissipative-Particle-Dynamics Simulations
2016
We propose a new model to simulate spherical colloids. This is a mesoscopic method based on the dissipative particle dynamics. The colloid is represented by a large spherical bead, and its surface interacts with the solvent beads through a pair of dissipative and stochastic forces. This new model extends the tunable-slip boundary condition [Eur. Phys. J. E 26, 115 (2008)] from planar surfaces to curved geometry, thus allows one to study colloids with slippery surfaces. Simulation results show good agreement with the prediction of hydrodynamic theories, indicating the hydrodynamic interactions are properly accounted in our new model.
Spinodal Decomposition Kinetics of Colloid-Polymer Mixtures Including Hydrodynamic Interactions
2012
The phase separation dynamics of a model colloid-polymer mixture is studied by taking explicitly the hydrodynamic interactions caused by the solvent into account. Based on the studies on equilibrium phase behavior we perform a volume quench from the homogeneous region of the phase diagram deep into the region where colloid-rich and polymer-rich phases coexist. We demonstrate that the Multiparticle Collision Dynamics (MPCD) algorithm is well suited to study spinodal decomposition and present first results on the domain growth behavior of colloid-polymer mixtures in quasi two-dimensional confinement. On the one hand side we find that the boundary condition of the solvent with respect to the r…
High Order Extrapolation Techniques for WENO Finite-Difference Schemes Applied to NACA Airfoil Profiles
2017
Finite-difference WENO schemes are capable of approximating accurately and efficiently weak solutions of hyperbolic conservation laws. In this context high order numerical boundary conditions have been proven to increase significantly the resolution of the numerical solutions. In this paper a finite-difference WENO scheme is combined with a high order boundary extrapolation technique at ghost cells to solve problems involving NACA airfoil profiles. The results obtained are comparable with those obtained through other techniques involving unstructured meshes.
Numerical propagator method solutions for the linear parabolic initial boundary-value problems
2007
On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial-boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial-boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi-implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are f…
The exact finite‐difference scheme for vector boundary‐value problems with piece‐wise constant coefficients
1998
We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schem…
Dynamic analysis for axially moving viscoelastic panels
2012
In this study, stability and dynamic behaviour of axially moving viscoelastic panels are investigated with the help of the classical modal analysis. We use the flat panel theory combined with the Kelvin–Voigt viscoelastic constitutive model, and we include the material derivative in the viscoelastic relations. Complex eigenvalues for the moving viscoelastic panel are studied with respect to the panel velocity, and the corresponding eigenfunctions are found using central finite differences. The governing equation for the transverse displacement of the panel is of fifth order in space, and thus five boundary conditions are set for the problem. The fifth condition is derived and set at the in-…