A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate

We present a level set approach to the numerical simulation of the Stefan problem on non-graded adaptive Cartesian grids, i.e. grids for which the size ratio between adjacent cells is not constrained. We use the quadtree data structure to discretize the computational domain and a simple recursive algorithm to automatically generate the adaptive grids. We use the level set method on quadtree of Min and Gibou [C. Min, F. Gibou, A second order accurate level set method on non-graded adaptive Cartesian grids, J. Comput. Phys. 225 (2007) 300–321] to keep track of the moving front between the two phases, and the finite difference scheme of Chen et al. [H. Chen, C. Min, F. Gibou, A supra-convergent finite difference scheme for the poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids, J. Sci. Comput. 31 (2007) 19–60] to solve the heat equations in each of the phases, with Dirichlet boundary conditions imposed on the interface. This scheme produces solutions that converge supralinearly (∼1.5)$(\sim 1.5)$ in both the L¹$L^1$ and the L^∞$L^{\infty }$ norms, which we demonstrate numerically for both the temperature field and the interface location. Numerical results also indicate that our method can simulate physical effects such as surface tension and crystalline anisotropy. We also present numerical data to quantify the saving in computational resources.     

Modeling snow crystal growth II: A mesoscopic lattice map with plausible dynamics

We present a local lattice model for the evolution of snow crystals that combines diffusion-limited aggregation with anisotropic attachment kinetics and an idealized quasi-liquid layer. Despite a voluminous modeling literature, this is apparently the first approach that successfully captures the essential form of core and tip instabilities, branch faceting, and other aspects of real snow crystal growth. As parameters are varied, our nearest neighbor system reproduces the basic features of most of the observed varieties of planar snowflakes and offers new insights into their genesis.     

A microscopic derivation of macroscopic sharp interface problems involving phase transitions

Macroscopic free boundary problems involving phase transitions (e.g., the classical Stefan problem or its modifications) are derived in a unified way from a Hamiltonian based on a general set of microscopic interactions. A Hamiltonian of the form + _x,x J(x–x)(x)(x) leads to differential equations as a result of Fourier transforms. Expanding the Fourier transform ofJ in powers ofq (the wave number), one can truncate the series at anarbitrary orderM, and thereby obtainMth-order differential equations. An asymptotic analysis of these equations in various scalings of the physical parameters then implies limits which are the standard macroscopic models for the dynamics of phase boundaries.     

A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem

In this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.     

On stable parametric finite element methods for the Stefan problem and the Mullins–Sekerka problem with applications to dendritic growth

We introduce a parametric finite element approximation for the Stefan problem with the Gibbs–Thomson law and kinetic undercooling, which mimics the underlying energy structure of the problem. The proposed method is also applicable to certain quasi-stationary variants, such as the Mullins–Sekerka problem. In addition, fully anisotropic energies are easily handled. The approximation has good mesh properties, leading to a well-conditioned discretization, even in three space dimensions. Several numerical computations, including for dendritic growth and for snow crystal growth, are presented.     

A volume of fluid approach for crystal growth simulation

A new approach to simulating the dendritic growth of pure metals, based on a recent volume of fluid (VOF) method with PLIC (piecewise linear interface calculation) reconstruction of the interface, is presented. The energy equation is solved using a diffuse-interface method, which avoids the need to apply the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to obtain the front velocity, are calculated with the aid of a distance function to the reconstructed interface. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by López et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Hernández et al. [Int. J. Numer. Methods Fluids 58 (2008) 897–921]), and the interface curvature is computed using an improved height function technique, which provides second-order accuracy. The proposed methodology is assessed by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.     

A review of iterative phase retrieval for measurement and encryption

Phase retrieval technique is regarded as one of the most significant tools to solve optical inverse problems. Several phase retrieval algorithms are discussed in this review. The occurrence of ill-posed conditions often makes the calculation difficult. As a synthesis, the multiple-image phase retrieval technology is invented to obtain more accurate convergence result in iterative computation. The multiple-input retrieval scheme can attach new constraints on convergence as a new limitation. As an indirect measuring method, it will make it possible to reconstruct the distribution of intensity and phase in an imaging or measurement system, where data processing is executed by computer. Moreover, the retrieval method has been applied for image encryption successfully. Finally, the development and application of the iterative phase retrieval are overviewed.     

A study of thermal, dielectric and magnetic properties of strontium malonate crystals

Crystals of strontium malonate (SrC₃H₂O₄) were grown in silica gel by the single diffusion technique. The thermo gravimetric (TG), differential thermal analysis (DTA) and differential scanning calorimetric (DSC) studies were carried out to investigate the thermal stability of the crystal. The dielectric behavior of the title compound crystal was investigated by measuring the dielectric parameters - dielectric constant, dielectric loss and AC conductivity as a function of four frequencies −1 kHz, 10 kHz, 100 kHz and 1 MHz at temperatures ranging from 50 to 170 °C. Results indicate that the title compound is thermally stable up to about 409 °C and is a promising low ε_r-value dielectric material. The magnetic behavior of the crystal was also explored using a vibrating sample magnetometer.     

研究椭圆积分物理问题的一种方法

在一些力学问题的研究中，严格的求解必须进行椭圆积分，这使问题变得复杂．但如果运用被积函数的某些性质，通过简单的数学运算，就可以化难为易，得到问题定性的、大致的结果．     

Prediction of a bcc-hcp phase transition for Sn: A first-principles study

The high-pressure structural transformation of elemental Sn is studied using an ab initio density functional theory implementation of the metadynamics method that predicts with sufficient compression, Sn will transform from the bcc structure into an hcp structure. The low-free-energy pathway associated with this phase transition is characterized as the Burgers transition mechanism. The superconducting properties of Sn under pressure are also investigated. Both bcc and hcp structures of Sn exhibit very weak electron-phonon coupling and therefore would not sustain superconductivity at high pressure.     

Structural,optical and mechanical property analysis of magnesium sulphate admixtured l-Threonine: A novel optoelectronic material

l-Threonine is an important amino acid and famous due to their property of frequency conversion and electro optic modulation. Single crystals of magnesium sulphate admixtured l-Threonine was grown by slow evaporation technique. Good quality single crystal with dimension 58 × 5 × 10 mm³ was harvested after 60 days. The powder X-ray diffraction pattern of the grown crystal has been indexed. The optical transmission spectrum shows that the magnesium sulphate admixtured l-Threonine possess good optical transparency in the entire visible region with Ultra Violet cut-off wavelength at 250 nm. The presence of fundamental functional groups was identified by Fourier Transform Infra Red spectral analysis. The structure of the grown crystal was established using Fourier Transform-Nuclear Magnetic Resonance spectral analysis. The thermal behaviour of the crystal has been discussed by Thermal Gravimetric Analysis and Differential Thermal Analysis. Magnesium sulphate admixtured l-Threonine was characterized by Energy dispersive analysis of X-ray. The second harmonic generation efficiency of magnesium sulphate admixtured l-Threonine crystal is found to be same as that of potassium dihydrogen phosphate crystal.     

Allowance for resonances in solving inverse and direct spectroscopic problems in an anharmonic approximation. A scheme of processing for experimental data

The most important aspects in solving inverse and direct spectroscopic problems in the second order of perturbation theory in the presence of Coriolis, Fermi, and Darling-Dennison resonances are discussed. A scheme for obtaining unperturbed values of spectroscopic parameters is suggested which has some advantages over that proposed earlier in [6]. It is believed that this information can be useful to specialists in the field of applied spectroscopy. Saratov State Technical University, 77, Politechnicheskaya St., Saratov, 410054, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 249–255, March–April, 1997.     

Exploration of pulse timing for multiple laser hits within a combined heat transfer, phase change, and gas dynamics model for laser ablation

Laser ablation involves heat transfer, phase changes and/or chemical reactions, and gas dynamics. All three of these processes are tightly coupled with each other. A model has previously been developed to simulate the nanosecond scale laser ablation of carbon. This model has been extended to accommodate longer term simulations and multiple laser pulses. The effects of varying the timing of a second laser pulse by tens of nanoseconds are explored. It is shown that by changing this interval one can control the total mass ablated and the mass transfer rate.     

Structural phase stability,electronic structure and mechanical properties of alkali metal hydrides AMH4 (A=Li,Na; M=B,AL)

The structural stability of Alkali metal hydrides AMH₄ (A=Li, Na; M=B, Al) is analyzed among the various crystal structures, namely hexagonal (P6₃mc), tetragonal (P4₂/nmc), tetragonal (P-42₁c), tetragonal (I4₁/a), orthorhombic (Pnma) and monoclinic (P2₁/c). It is observed that, orthorhombic (Pnma) phase is the most stable structure for LiBH₄, monoclinic (P2₁/c) for LiAlH₄, tetragonal (P4₂/nmc) for NaBH₄ and tetragonal (I4₁/a) for NaAlH₄ at normal pressure. Pressure induced structural phase transitions are observed in LiBH₄, LiAlH₄, NaBH₄ and NaAlH₄ at the pressures of 4 GPa, 36.1 GPa, 26.5 GPa and 46 GPa respectively. The electronic structure reveals that these metal hydrides are wide band gap insulators. The calculated elastic constants indicate that these metal hydrides are mechanically stable at normal pressure.     

A new formulation of Kapila’s five-equation model for compressible two-fluid flow,and its numerical treatment

A new formulation of Kapila’s five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The new formulation uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which exchange terms are derived from physical laws. All equations are written as a single system of equations in integral form. No equation is used to describe the topology of the two-fluid flow. Relations for the Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the exchange terms is proposed. The exchange terms have distinct contributions in the cell interior and at the cell faces. For the exchange-term evaluation at the cell faces, the same Riemann solver as used for the flux evaluation is exploited. Numerical results are presented for two-fluid shock-tube and shock-bubble-interaction problems, the former also for a two-fluid mixture case. All results show good resemblance with reference results.     

A novel method for the assembly of nano-zeolite crystals on porous stainless steel microchannel and then zeolite film growth

A new method that is simple, efficient, and clean was developed for seeding surfaces with a monolayer of covalently bonded zeolite seeds. This method was used to seed the microchannels fabricated on porous stainless steel with NaA nano-zeolites enabling the deposition and growth of defect-free zeolite film. The NaA nano-zeolites were attached to the surface of the stainless steel via alkoxysilane linkers (e.g., 3-chloropropyltrimethoxysilane and 3-aminopropyltrimethoxysilane) grafted on the stainless steel. The NaA zeolite grown on the microchannel by hydrothermal synthesis consists of intergrown, (1 1 1)-oriented pyramidal NaA crystals that completely clad the stainless steel grains. The zeolite cladding the grains grew uniformly until the zeolite layers of neighboring grain impinges, then intergrew to fully bridge the gaps between the grains forming a defect-free film layer. A separation factor of 10,000 and a flux of 0.04 kg m⁻² h⁻¹ were obtained for water pervaporation from a 3 wt% water-benzaldehyde solution at room temperature.     

Solvated fullerenes,a new class of carbon materials suitable for high-pressure studies: A review

As the list of known carbon compounds grows longer, solvated fullerenes have become a more important class of carbon materials. Their general properties and methods of synthesis have both attracted considerable attention. The study of the behavior of these compounds under high-pressure conditions has revealed several new phenomena that have never been observed in pure fullerene. This article is a review of all recent progress in this field.     

Observation of three sites for vanadyl in a biomineral, zinc sodium phosphate hexahydrate: an EPR investigation

Single crystal EPR study has been carried at room temperature for VO(II) doped zinc sodium phosphate hexahydrate. Single crystal rotations in each of the three mutually orthogonal crystallographic planes namely bc, ac, and ab indicate three chemically inequivalent sites, with intensity ratios of 25:13:1. The spin Hamiltonian parameters obtained for the two intense sites are: Site I: g_xx=1.983, g_yy=1.985, g_zz=1.933; A_xx=7.39 mT, A_yy=7.15 mT, A_zz=19.03 mT; Site. II: g_xx=1.985, g_yy=1.985, g_zz=1.937; A_xx=7.36 mT, A_yy=7.25 mT, A_zz=18.67 mT. The two VO bond directions in the two sites are approximately at right angles to each other. The powder spectrum clearly indicates two chemically inequivalent sites, confirming the single crystal analysis. Admixture coefficients, Fermi contact, and dipolar interaction terms have also been evaluated.     

Tetrahedral coordination for Zn in hexacyanometallates: Structures of Zn3A2[M(CN)6]2·xH2O with A=K, Rb, Cs and M=Ru, Os

Zinc hexacyanoruthenate (II) and hexacyanoosmate (II) were prepared and studied from X-ray diffraction (XRD), infrared (IR), and thermogravimetric (TG) data. These compounds were found to be isomorphous with the iron analogues, crystallizing with a rhombohedral unit cell (R−3c space group), where the zinc atom has tetrahedral coordination to N ends of CN groups. For Cs, compounds with formula unit ZnCs₂[M(CN)₆] and a cubic unit cell (Fm−3m) were also obtained. The crystal structures for the eight compositions were refined from the corresponding X-ray powder diffraction patterns using the Rietveld method. Related to the tetrahedral coordination for the Zn atom, the rhombohedral phase has a porous framework with ellipsoidal cavities of about 12.5×9×8 Å, communicated by elliptical windows of ∼5 Å. Within these cavities the exchangeable alkali metal ions are found. The filling of the cavity volume is completed with water molecules. IR spectrum senses certain charge delocalization from the inner metal, through the π-back donation mechanism. For Os compounds this effect is particularly pronounced, related to a more diffuse d orbitals for this metal.