A moving boundary model motivated by electric breakdown: II. Initial value problem

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a ‘kinetic undercooling’ boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for t→∞, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time.     

Generation of laser-driven flyer dominated by shock-induced shear bands: A molecular dynamics simulation study

High-power pulsed lasers provide an ingenious method for launching metal foils to generate high-speed flyers for high-pressure loading in material science or aerospace engineering.At high-temperature and high-pressure laser-induced conditions,the dynamic response of the metals and the mechanism of flyer formation remain unclear.In this study,the overall process of the laser-driven aluminum flyer,including laser ablation,rupture of metal foil,and the generation of the flyer was investigated by molecular dynamics combined with the two-temperature model.It was found that under high laser fluence(over 1.3 J/cm;with 200-fs laser pulse duration),the laser induced a shock wave with a peak pressure higher than25 GPa,which led to shear bands expanding from the edge of the laser ablation zone in the foil.Compared with the cases of low laser fluence less than 0.5 J/cm^-1,the shear band induced by high laser fluence promotes the rupture of the foil and results in a high-speed flyer(>1 km/s)with better flatness and integrity.In addition,the shock wavefront was found to be accompanied by aluminum crystal phase transformation from face-centered cubic(FCC)to body-centered cubic structure.The crystal structure reverts with the decrease of pressure,therefore the internal structure of the generated flyer is pure of FCC.The results of this study provide a better understanding of the laser-induced shock effect on the foil rupture and flyer quality and forward the development of the laser-driven flyer.     

A model phospholipid monolayer: a computer simulation study

A phospholipid monolayer is modelled by quasi two-dimensional hard dipoles. The dipole interactions are three-dimensional and the two continuous phases are characterized by their dielectric constants. A tendency of dipolar chain formation is observed for low temperatures and for equal dielectric constants. This tendency disappears when the two regions are slightly different.     

Numerical simulation of catalytic combustion of methane using washcoat model and external model: a comparison study

This paper presents a comparison study of numerical simulation of catalytic combustion of methane on Pt catalyst using two different physical models. The external surface model and the washcoat model were employed. The simulations were conducted in a two-dimensional monolith reactor with detail surface kinetics. The agreement of simulation results of the washcoat model with the measured data is good. However, in contrast to experimental data, the external surface method will produce a lower result of conversion of CH₄ at low temperature due to the neglecting of the larger inner surface of the washcoat. Moreover, the effects of specific surface area and pore size of washcoat on reaction rate were discussed. It can be concluded that the washcoat model would provide a more realistic result and can enrich the contents of numerical simulation of catalytic reaction.     

A new magneto-cardiogram study using a vector model with a virtual heart and the boundary element method

A cardiac vector model is presented and verified, and then the forward problem for cardiac magnetic fields and electric potential are discussed based on this model and the realistic human torso volume conductor model, including lungs. A torso-cardiac vector model is used for a 12-lead electrocardiographic (ECG) and magneto-cardiogram (MCG) simulation study by using the boundary element method (BEM). Also, we obtain the MCG wave picture using a compound four-channel HTc ·SQUID system in a magnetically shielded room. By comparing the simulated results and experimental results, we verify the cardiac vector model and then do a preliminary study of the forward problem of MCG and ECG. Therefore, the results show that the vector model is reasonable in cardiac electrophysiology.     

A study of Barstar folding events using boundary value simulations

From extensive biophysical studies of protein folding, two competing mechanisms emerged: hydrophobic collapse and the framework model. Our protein of choice is Barstar—a barnase inhibitor. The approximation algorithm we used to study Barstar folding trajectories is called SDEL—stochastic difference equation in length. Using the native structure as the final boundary value and a collection of unfolded structures as the varying initial boundary value, SDEL calculates an ensemble of least action pathways between these boundaries. The results are atomically detailed folding pathways, with as many intermediate structures as you request in the input. We generated 12 pathways, starting from a structurally wide selection of unfolded conformations. Using the protein's radius of gyration as our primary reaction coordinate, we tracked H-bonds, dihedral angles, native and non-native contacts, and energy along the folding pathways. This paper will follow our findings, with special emphasis on pinpointing hydrophobic collapse as a more appropriate mechanism for Barstar. Comparison with pathway predictions for Barstar using experimental techniques will also be discussed.     

Computer simulation of topological effects in lattice theories: A model study

The quantum pendulum as a model is put on a lattice, producing a straightforward definition of topological charge. It is used to single out non-perturbative effects in a Monte Carlo calculation and compare them with a semiclassical picture. The method of subtracting perturbative contributions from numerical results recently used for the gluon condensate is tested.     

大气边界层各向异性的室内模拟研究

 边界层的各向异性研究对于了解实际大气的湍流特性和经典理论的适用范围均具有较大的意义。利用室内水槽实验模拟了实际大气边界层,使用小波变换方法分析了对数光强起伏谱的特征,将获得的标度指数与理论值进行比较,结果表明混合层在水平方向较为接近各向同性,而垂直方向则呈现一定的各向异性。     

大气边界层各向异性的室内模拟研究

边界层的各向异性研究对于了解实际大气的湍流特性和经典理论的适用范围均具有较大的意义。利用室内水槽实验模拟了实际大气边界层,使用小波变换方法分析了对数光强起伏谱的特征,将获得的标度指数与理论值进行比较,结果表明混合层在水平方向较为接近各向同性,而垂直方向则呈现一定的各向异性。     

The valence bands of model amorphous semiconductor structures

Using a basis of bonding orbitals, and tight-binding matrix elements which depend on the local topology, we calculate the valence band electronic structure of silicon on the diamond and ST12(GeIII) lattices, as well as on the continuous random networks of Polk and Boudreaux and Connell and Temkin. Results indicate the need for odd-membered rings to account for the experimentally observed features.     

Phase-field models for moving boundary problems: Controlling metastability and anisotropy

We introduce a variant of a recently proposed method of rotated lattices for numerical treatment of moving boundary problems. The usual lattice introduced for numerical computation of phase-field models gives rise to unphysical metastable states and anisotropy. In the present case we rotate and shift the lattice by random angles and fractions of a lattice constant. We show that a twelve point interpolation formula is adequate to keep numerical interpolation errors sufficiently localized. This removes the unphysical metastabilities and makes the model fully isotropic. This is demonstrated by a few example-calculations for dendritic pattern formation.     

A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation

In this paper, a new lattice model of traffic flow is proposed to investigate wide moving jams in traffic flow with the consideration of the driver anticipation information about two preceding sites. The linear stability condition is obtained by using linear stability analysis. The mKdV equation is derived through nonlinear analysis, which can be conceivably taken as an approximation to a wide moving jam. Numerical simulation also confirms that the congested traffic patterns about wide moving jam propagation in accordance with empirical results can be suppressed efficiently by taking the driver anticipation effect of two preceding sites into account in a new lattice model.     

Impurity bands in semiconductors: A further study of three-impurity clusters

Ionization energies and electron affinities of three-impurity systems are computed variationally. Correlation is taken into account within the spin-density functional formalism. The results strongly support the recent suggestion that broadening of the lower Hubbard band is responsible for the closing of the Mott—Hubbard gap with increasing impurity concentration.     

Acoustic boundary layer influence on scale model simulation of sound propagation: Theory and numerical examples

Scale model simulation of sound propagation above a solid surface will give a systematic and calculable error in the predicted sound field, because the acoustic boundary layer above the surface has an apparent admittance which is not invariant under scaling. The typical error is approximately 5 dB depending on the geometrical configuration, scale and frequency. The effect of the acoustic boundary layer admittance is negligible for sound propagation above an acoustically soft surface (e.g., grassland). One may moreover note, with reference to scale model simulation of concert hall acoustics, that the absorption coefficient of a solid surface increases with frequency.     

Fictitious domains and level sets for moving boundary problems. Applications to the numerical simulation of tumor growth

In this work we present a new strategy for solving numerically a (relatively simple) model of tumor growth. In principle, this is devoted to describe avascular growth although, by choosing the parameters appropriately, it also permits to give an idea of the behavior after vascularization. The numerical methods rely on fictitious domain and level set techniques, with a combination of quadratic finite elements and finite differences approximations. We present a collection of numerical results that essentially coincide with others, previously obtained with other techniques.     

The moving boundary node method: A level set-based,finite volume algorithm with applications to cell motility

Eukaryotic cell crawling is a highly complex biophysical and biochemical process, where deformation and motion of a cell are driven by internal, biochemical regulation of a poroelastic cytoskeleton. One challenge to built quantitative models that describe crawling cells is solving the reaction–diffusion–advection dynamics for the biochemical and cytoskeletal components of the cell inside its moving and deforming geometry. Here we develop an algorithm that uses the level set method to move the cell boundary and uses information stored in the distance map to construct a finite volume representation of the cell. Our method preserves Cartesian connectivity of nodes in the finite volume representation while resolving the distorted cell geometry. Derivatives approximated using a Taylor series expansion at finite volume interfaces lead to second order accuracy even on highly distorted quadrilateral elements. A modified, Laplacian-based interpolation scheme is developed that conserves mass while interpolating values onto nodes that join the cell interior as the boundary moves. An implicit time stepping algorithm is used to maintain stability. We use the algorithm to simulate two simple models for cellular crawling. The first model uses depolymerization of the cytoskeleton to drive cell motility and suggests that the shape of a steady crawling cell is strongly dependent on the adhesion between the cell and the substrate. In the second model, we use a model for chemical signalling during chemotaxis to determine the shape of a crawling cell in a constant gradient and to show cellular response upon gradient reversal.     

Negative parity rotational bands in28Si: A cluster model approach

Describing the expanding fireballs in a relativistic gas dynamical approach the formation of deuterons is calculated under consideration of inmedium corrections. The theoretical results are in good agreement with experimental data.     

The boundary of a boundary principle: A unified approach

The boundary of a boundary principle in field theories is described. The difference in treatment of the principle in electrodynamics and general relativity is pointed out and reformulated in terms of underlying mathematical structure of the theories. The problem of unifying the treatment is formulated and solved. The role of E. Cartan's concept of the moment of rotation associated with the curvature of a Levi-Civita connection on a frame bundle is shown to be crucial for the unification. The analysis of the boundary of a boundary principle in Kaluza-Klein theory is performed and the recipe for a unified treatment of the principle in electrodynamics and general relativity is shown to follow from the analysis. It is pointed out that the unification cand be extended to Yang-Mills fields easily.