Computation of nonlinear multiscale coupling effects in liquid phase epitaxy

A new two-scale model for liquid phase epitaxy is presented which enables the numerical simulation of processes with microstructures having an arbitrarily small scale. It is based on a BCF-model for epitaxial growth, a Navier–Stokes system and a convection-diffusion equation. The application of a homo- genization approach leads to a separation of scales; the resulting two-scale model consists of macroscopic partial differential equations for fluid flow and solute diffusion in the fluid volume, coupled to microscopic BCF-models. The two-scale model can be discretized using grids that are independent of the scale of the microstructure. Numerical experiments based on a phase field version of the BCF model are presented; the results illustrate the physical relevance of the model.     

Computation of solidification problems with hydrodynamic convection resolving energetic anisotropies at the microscale quantitatively

In this work we propose a new numerical approach to solve the solidification of microstructures from a pure melt including hydrodynamic effects in the molten phase. The model is based on the classical sharp-interface model, i.e the solid–liquid interface is tracked and latent heat is released. An enhanced scheme is employed to solve fluid flow in the melt. The no-slip condition is applied on the interface by enforcing the velocities in the solid phase to be zero. The morphology evolution of the solidifying crystal microstructure under the influence of convection is compared with an existing morphology diagram for pure diffusion controlled growth (see Brener et al. [1]). The peculiarity of our approach is that it models the physical anisotropies along the solid–liquid interface with high accuracy. This allows us to report changes in the morphology diagram given by Brener et al. [1] due to the influence of forced flow. Moreover, we present some results on the scaling of the dendritic tip in such cases.     

Stochastic Burgers and KPZ Equations from Particle Systems

We consider two strictly related models: a solid on solid interface growth model and the weakly asymmetric exclusion process, both on the one dimensional lattice. It has been proven that, in the diffusive scaling limit, the density field of the weakly asymmetric exclusion process evolves according to the Burgers equation and the fluctuation field converges to a generalized Ornstein-Uhlenbeck process. We analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the (non linear) Burgers equation with a random noise on the density current. For the solid on solid model, we prove that the fluctuation field of the interface profile, if suitably rescaled, converges to the Kardar–Parisi–Zhang equation. This provides a microscopic justification of the so called kinetic roughening, i.e. the non Gaussian fluctuations in some non-equilibrium processes. Our main tool is the Cole-Hopf transformation and its microscopic version. We also develop a mathematical theory for the macroscopic equations. Received: 24 October 1995/Accepted: 9 July 1996     

Mean Field Analysis of Low–Dimensional Systems

For low–dimensional systems, (i.e. 2D and, to a certain extent, 1D) it is proved that mean–field theory can provide an asymptotic guideline to the phase structure of actual systems. In particular, for attractive pair interactions that are sufficiently “spead out” according to an exponential (Yukawa) potential it is shown that the energy, free energy and, in particular, the block magnetization (as defined on scales that are large compared with the lattice spacing but small compared to the range of the interaction) will only take on values near to those predicted by the associated mean–field theory. While this applies for systems in all dimensions, the significant applications are for d = 2 where it is shown: (a) If the mean–field theory has a discontinuous phase transition featuring the breaking of a discrete symmetry then this sort of transition will occur in the actual system. Prominent examples include the two–dimensional q = 3 state Potts model. (b) If the mean–field theory has a discontinuous transition accompanied by the breaking of a continuous symmetry, the thermodynamic discontinuity is preserved even if the symmetry breaking is forbidden in the actual system. E.g. the two–dimensional O(3) nematic liquid crystal. Further it is demonstrated that mean–field behavior in the vicinity of the magnetic transition for layered Ising and XY systems also occurs in actual layered systems (with spread–out interactions) even if genuine magnetic ordering is precluded.     

Renormalization Group Approach to Multiscale Modelling in Materials Science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation—a conserving analogue of the Swift-Hohenberg equation—is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms. PACS numbers: 81.16.Rf, 05.10.Cc, 61.72.Cc, 81.15.Aa     

Correlated wave functions to approach the bound excited states of Li- and Be-

Explicitly correlated wave functions including a Jastrow factor to take into account the dynamical correlation effects, and a multi determinant model wave function to account for the non–dynamical correlations are used to study some metastable excited states of the negative ions Li^- and Be^-. A detailed analysis of one– and two–body properties has been carried out for these states. In particular the single–particle density as well as both the two–body inter electronic and center of mass densities have been obtained. All the calculations have been performed by using the variational Monte Carlo method.     

Thermodynamic properties of gold–water nanolayer mixtures using molecular dynamics

The physical behavior of a fluid in contact with solid layers is still not fully understood. The present work focuses on the study and understanding of thermodynamic and structural properties of gold–water nanolayer mixtures using molecular dynamics simulations. Two different systems are considered, where approximately 1,700 water molecules are confined between gold nanolayers with separations of 7.4 and 6.2 nm, respectively. Novelties of the present work are in the use of accurate force fields for modeling the inter- and intra-molecular interactions of the components, and providing comprehensive thermodynamic properties of the mixtures. The results are validated by examination of the pure fluid and pure solid properties. Results indicate that the thermodynamics of the system does not behave as an ideal mixture. The structure of the pure fluid is also analyzed and compared against the structure of the confined fluid in the mixture. Anisotropicity is observed in the fluid structure close to the surface of the nanolayer. Higher ordering and higher flux are detected in the fluid molecules close to the fluid–solid interface. Unusual thermodynamic behavior, anisotropicity, liquid layering, and higher interfacial fluid flux could be just some of the factors leading to the enhanced energy transport observed in mixtures involving at least one nanoscale component, such as nanofluids.     

Identification of a low-frequency elastic behaviour in liquid water

This article deals with the identification of solid-like properties measured at room temperature at a sub-millimetre length scale in liquid water. At a macroscopic scale, normal liquids (i.e.?above melting temperature), and in particular water, are typically and empirically defined by the absence of shear elasticity, in contrast to solids or plastic fluids that require a stress threshold for flowing. A novel method optimizing the transmission of the shear stress to the sample enables a more complete probe of the mechanical response of liquids. It reveals that glass formers and viscous alkanes actually exhibit finite macroscopic shear elasticity away from any phase transition. This protocol is here applied for the first time to liquid water at room temperature, revealing, at the sub-millimetre scale, a low-frequency solid-like property.     

A nonlinear macroscopic multi-phasic model for describing interactions between solid,fluid and ionic species in biological tissue materials

A nonlinear, macroscopic multi-phasic model for describing the interactions between solid, fluid, and ionic species in porous materials is presented. Governing equations are derived based on the nonlinear theories of solid mechanics, linear flow theory of Newtonian fluids, and theory of irreversible thermodynamics for the transport of ions and ionic solutions. The model shows that the transport coupling between ions and ionic solution exists only when the porous material has a membrane-like feature, which could be inside the material or on the material boundaries. Otherwise, the coupling occurs only between the solid and fluid phases and the transport of ionic species will have no effect on the macroscopic stresses, strains and displacements of the porous material. As an application of the present multi-phasic model, a numerical example of the human cornea under the shock of NaCl hypertonic solution applied to its endothelial surface is presented. This is a typical example of how ionic transport induces swelling in biological tissues. The results obtained from the present multi-phasic model demonstrate that the mechanical properties of the tissue have an important influence on the swelling of the cornea. Without taking into account this influence, the predicted swelling may be exaggerated.     

Reconstructing the chargino system at e^+e^- linear colliders

In most supersymmetric theories charginos, , belong to the class of the lightest supersymmetric particles. The chargino system can be reconstructed completely in collider experiments: . By measuring the total cross sections and the asymmetries with polarized beams, the chargino masses and the gaugino–higgsino mixing angles of these states can be determined accurately. If only the lightest charginos are kinematically accessible in a first phase of the machine, transverse beam polarization or the measurement of chargino polarization in the final state is needed to determine the mixing angles. From these observables the fundamental SUSY parameters can be derived: the SU(2) gaugino mass , the modulus and the cosine of the CP–violating phase of the higgsino mass parameter , and , the ratio of the vacuum expectation values of the two neutral Higgs doublet fields. The remaining two–fold ambiguity of the phase can be resolved by measuring the normal polarization of the charginos. Sum rules of the cross sections can be exploited to investigate the closure of the two–chargino system. Received: 2 February 2000 / Published online: 17 March 2000     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

Thermodynamics and surface properties of liquid Al–Ga and Al–Ge alloys

The surface properties of Al–Ga and Al–Ge liquid alloys have been theoretically investigated at a temperature of 1100 K and 1220 K respectively. For the Al–Ga system, the quasi chemical model for regular alloy and a model for phase segregating alloy systems were applied, while for the Al–Ge system the quasi chemical model for regular and compound forming binary alloys were applied. In the case of Al–Ga, the models for the regular alloys and that for the phase segregating alloys produced the same value of order energy and same values of thermodynamic and surface properties, while for the Al–Ge system, the model for the regular alloy reproduced better the thermodynamic properties of the alloy. The model for the compound forming systems showed a qualitative trend with the measured values of the thermodynamic properties of the Al–Ge alloy and suggests the presence of a weak complex of the form Al₂Ge₃. The surface concentrations for the alloys show that Ga manifests some level of surface segregation in Al–Ga liquid alloy while the surface concentration of Ge in Al–Ge liquid alloy showed a near Roultian behavior below 0.8 atomic fraction of Ge.     

尺寸效应对微通道内固液界面温度边界的影响

采用非平衡分子动力学方法模拟不同浸润性微通道内液体的传热过程,分析了尺寸效应对固液界面热阻及温度阶跃的影响.研究结果表明,界面热阻随微通道尺寸的变化可分为两个阶段,即小尺寸微通道的单调递增阶段和大尺寸微通道的恒定值阶段.随着微通道尺寸的增加,近壁区液体原子受对侧固体原子的约束程度降低,微通道中央的液体原子自由移动,固液原子振动态密度近似不变,使得尺寸效应的影响忽略不计.上述两种阶段的微通道尺寸过渡阈值受固液作用强度与壁面温度的共同作用:减弱壁面浸润性,过渡阈值向大尺寸区域迁移;相较于低温壁面,高温壁面处的过渡阈值更大.增加微通道尺寸,固液界面温度阶跃呈单调递减趋势,致使壁面温度边界和宏观尺度下逐渐符合.探讨尺寸效应有助于深刻理解固液界面能量输运及传递机制.     

Nonminimally coupled scalar field and perfect fluid in Einstein–Cartan cosmology

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field and perfect fluid. Some effects of torsion are revealed by solving an analogous problem in general relativity. A comparative analysis of the cosmological models with and without perfect fluid is carried out in context of the Einstein–Cartan theory. The role of perfect fluid in the dynamics of models is discussed.     

Formation of multilayer strained-layer heterostructures by liquid epitaxy. I. Theoretical aspects of the problem and mathematical model

Problems concerned with the formation of multilayer strained-layer heterostructures by “capillary” liquid-phase epitaxy with forced hydraulic replacement of the solutions in the growth channel are analyzed. It is shown for short contact times between the solutions and the crystallization surface that the character of their flow in the channel plays an important role in the achievement of uniformity in the physical characteristics of the layers grown. Theoretical estimates of the hydrodynamic stability of solutions moving in narrow channels are performed for several III-V systems. A mathematical model, which permits simulation of the conditions under which strained-layer heterostructures are fabricated, is developed. It takes into account diffusive and convective mass transport in the liquid for various flow regimes in the capillary and the displacement of the heterogeneous equilibria in the system under the influence of elastic stresses. Zh. Tekh. Fiz. 67, 42–49 (July 1997)     

Diffusive Fluctuations for One-Dimensional Totally Asymmetric Interacting Random Dynamics

We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous–Diaconis–Hammersley process and the related stick model. The A-D-H process represents a particle configuration on the line, or a 1-dimensional interface on the plane which moves in one fixed direction through random local jumps. The stick model is the process of local slopes of the A-D-H process, and has a conserved quantity. The results describe the fluctuations of these systems around the deterministic evolution to which the random system converges under hydrodynamic scaling. We look at diffusive fluctuations, by which we mean fluctuations on the scale of the classical central limit theorem. In the scaling limit these fluctuations obey deterministic equations with random initial conditions given by the initial fluctuations. Of particular interest is the effect of macroscopic shocks, which play a dominant role because dynamical noise is suppressed on the scale we are working. Received: 4 October 2001 / Accepted: 12 March 2002     

The kinetics of homogeneous nucleation of silver nanoparticles stabilized by polymers

The formation of Ag nanoparticles synthesized by homogeneous nucleation, stabilized by polymers (PVA and PVP) was monitored by UV–Vis spectrophotometry and transmission electron microscopy. Our aim was to differentiate between the two main phases of particle formation, i.e. nucleation and growth and to characterize their rates with the help of appropriate kinetic equations. Time resolved spectrophotometric measurements revealed that particle formation is an autocatalytic process: a slow, continuous nucleation phase (3–5 min) is followed by a rapid, autocatalytic growth phase where the maximal particle size is 5–7 nm. By freezing the reaction mixture, the process of particle growth can be followed from 5 to 40 min on TEM pictures. The first order rate constants were calculated and they are strongly depend on the polymer concentration. If the growing particles are attached by PEI to the surface of a solid support, the formation of silver nanoparticles can also be followed by atomic force microscopy (AFM) and we can control the particle growth on mica surface. The cross section analysis of the pictures show, that the particle growing process can be also monitored at solid–liquid interface.