Une méthode multiniveau pour la simulation des grandes échelles des écoulements turbulents compressibles

A multilevel method for Large-Eddy Simulation of turbulent unsteady compressible flows is proposed. It relies on the splitting of the turbulent flowfield into several frequency bands in space and time, each band being associated to a computational grid in physical space, allowing to take into account in a deterministic way the information contained on finer grids. A subgrid-scale model adapted to such a decomposition — based on a generalization of the Germano's identity to multilevel decomposition — is also introduced. The approach is validated by a simulation in a subsonic plane channel flow configuration.     

Adaptive multilevel finite element solution of the Poisson–Boltzmann equation I. Algorithms and examples

This article is the first of two articles on the adaptive multilevel finite element treatment of the nonlinear Poisson–Boltzmann equation (PBE), a nonlinear eliptic equation arising in biomolecular modeling. Fast and accurate numerical solution of the PBE is usually difficult to accomplish, due to the presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domain, and rapid (exponential) nonlinearity. In this first article, we explain how adaptive multilevel finite element methods can be used to obtain extremely accurate solutions to the PBE with very modest computational resources, and we present some illustrative examples using two well‐known test problems. The PBE is first discretized with piece‐wise linear finite elements over a very coarse simplex triangulation of the domain. The resulting nonlinear algebraic equations are solved with global inexact Newton methods, which we have described in an article appearing previously in this journal. A posteriori error estimates are then computed from this discrete solution, which then drives a simplex subdivision algorithm for performing adaptive mesh refinement. The discretize–solve–estimate–refine procedure is then repeated, until a nearly uniform solution quality is obtained. The sequence of unstructured meshes is used to apply multilevel methods in conjunction with global inexact Newton methods, so that the cost of solving the nonlinear algebraic equations at each step approaches optimal O(N) linear complexity. All of the numerical procedures are implemented in MANIFOLD CODE (MC), a computer program designed and built by the first author over several years at Caltech and UC San Diego. MC is designed to solve a very general class of nonlinear elliptic equations on complicated domains in two and three dimensions. We describe some of the key features of MC, and give a detailed analysis of its performance for two model PBE problems, with comparisons to the alternative methods. It is shown that the best available uniform mesh‐based finite difference or box‐method algorithms, including multilevel methods, require substantially more time to reach a target PBE solution accuracy than the adaptive multilevel methods in MC. In the second article, we develop an error estimator based on geometric solvent accessibility, and present a series of detailed numerical experiments for several complex biomolecules. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1319–1342, 2000     

Explicit form of determinants and inverse matrices of Tribonacci <Emphasis Type="Italic">r</Emphasis>-circulant type matrices

The determinants and inverses of Tribonacci r-circulant type matrices are discussed in the paper. Firstly, Tribonacci r-circulant type matrices are defined. In addition, we show the invertibility of the Tribonacci r-circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between r-circulant and r-left circulant, the invertibility of the Tribonacci r-left circulant matrix are also discussed. Finally, the determinants and the inverse matrices of the these matrices are given, respectively.     

Multilevel augmentation method with wavelet bases for singularly perturbed problem

Multilevel augmentation method with wavelet bases is demonstrated to show as the fast technique for solving singularly perturbed problems. Linear and quadratic wavelet bases are employed for constructing the full form of matrix system. To reduce the size of matrix coefficients, the multilevel augmented technique is applied at each current basis level. It is found that the multilevel augmentation method is faster than the standard multilevel method at the same order of accuracy. Convergent rates for linear and quadratic bases are 2 and 4 respectively. By the application of wavelet bases, numerical accuracy can be easily improved by increasing just desired levels in the multilevel augmentation process.     

A Novel Bat‐Shaped Dicyanomethylene‐4H‐pyran‐Functionalized Naphthalimide for Highly Efficient Solution‐Processed Multilevel Memory Devices

Small‐molecule‐based multilevel memory devices have attracted increasing attention because of their advantages, such as super‐high storage density, fast reading speed, light weight, low energy consumption, and shock resistance. However, the fabrication of small‐molecule‐based devices always requires expensive vacuum‐deposition techniques or high temperatures for spin‐coating. Herein, through rational tailoring of a previous molecule, DPCNCANA (4,4′‐(6,6′‐bis(2‐octyl‐1,3‐dioxo‐2,3‐dihydro‐1H‐benzo[de]isoquinolin‐6‐yl)‐9H,9′H‐[3,3′‐bicarbazole]‐9,9′‐diyl)dibenzonitrile), a novel bat‐shaped A‐D‐A‐type (A‐D‐A=acceptor–donor–acceptor) symmetric framework has been successfully synthesized and can be dissolved in common solvents at room temperature. Additionally, it has a low‐energy bandgap and dense intramolecular stacking in the film state. The solution‐processed memory devices exhibited high‐performance nonvolatile multilevel data‐storage properties with low switching threshold voltages of about −1.3 and −2.7 V, which is beneficial for low power consumption. Our result should prompt the study of highly efficient solution‐processed multilevel memory devices in the field of organic electronics.     

Rotational fluctuation of molecules in quantum clusters. I. Path integral hybrid Monte Carlo algorithm

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.     

Molecular Networks in Dynamic Multilevel Systems

Dynamic multilevel systems can be assembled from molecular building blocks through two or more reversible reactions that form covalent bonds. Molecular networks of dynamic multilevel systems can exhibit different connectivities between nodes. The design and creation of molecular networks in multilevel systems require control of the crossed reactivity of the functional groups (how to connect nodes) and the conditions of the reactions (when to connect nodes). In recent years, the combination of orthogonal and communicating reactions, which can be simultaneous or individually activated, has produced a variety of systems that have given rise to macrocycles and cages, as well as molecular motors and multicomponent architectures on surfaces. A given set of reactions can lead to systems with unique responsiveness, compositions, and functions as a result of the relative reactivities. In this Concept article, different molecular networks from synthetic systems that can be produced by combinations of different reaction types are discussed. Moreover, applications of this chemistry are highlighted, and future perspectives are envisioned.     

Towards Highly‐Efficient Phototriggered Data Storage by Utilizing a Diketopyrrolopyrrole‐Based Photoelectronic Small Molecule

A cooperative photoelectrical strategy is proposed for effectively modulating the performance of a multilevel data‐storage device. By taking advantage of organic photoelectronic molecules as storage media, the fabricated device exhibited enhanced working parameters under the action of both optical and electrical inputs. In cooperation with UV light, the operating voltages of the memory device were decreased, which was beneficial for low energy consumption. Moreover, the ON/OFF current ratio was more tunable and facilitated high‐resolution multilevel storage. Compared with previous methods that focused on tuning the storage media, this study provides an easy approach for optimizing organic devices through multiple physical channels. More importantly, this method holds promise for integrating multiple functionalities into high‐density data‐storage devices.     

Bioinspired synthesis and preparation of multilevel micro/nanostructured materials

In this review, some living organisms with multilevel hierarchical micro/nanostructures and related special properties are briefly introduced. The unique properties of organisms are mostly related to their special hierarchical micro/nanostructures. Inspired by nature, many zero-dimensional and one-dimensional micro/nanomaterials with biomimic or bioinspired multilevel micro/nanostructures have been successfully synthesized and prepared in recent years. Compared with traditional solid materials, the synthesis and preparation of these multilevel structured materials is more ingenious. Moreover, these kinds of multilevel micro/nanomaterials show fantastic properties in many fields because of their micro/nanoscale complex interior structures, whichmay be intended for application in catalysis, Li-ion batteries, biomedicines, sensors, and others.     

Condensed-phase relaxation of multilevel quantum systems. I. An exactly solvable model

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.     

Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods

We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in an article appearing previously in this journal. A detailed analysis of the resulting method is presented, with comparisons to other methods that have been proposed in the literature, including the classical nonlinear multigrid method, the nonlinear conjugate gradient method, and nonlinear relaxation methods such as successive overrelaxation. Both theoretical and numerical evidence suggests that this method will converge in the case of molecules for which many of the existing methods will not. In addition, for problems which the other methods are able to solve, numerical experiments show that the new method is substantially more efficient, and the superiority of this method grows with the problem size. The method is easy to implement once a linear multilevel solver is available and can also easily be used in conjunction with linear methods other than multigrid. © 1995 by John Wiley & Sons, Inc.     

Adaptive multilevel finite element solution of the Poisson–Boltzmann equation II. Refinement at solvent‐accessible surfaces in biomolecular systems

We apply the adaptive multilevel finite element techniques (Holst, Baker, and Wang 21 ) to the nonlinear Poisson–Boltzmann equation (PBE) in the context of biomolecules. Fast and accurate numerical solution of the PBE in this setting is usually difficult to accomplish due to presence of discontinuous coefficients, delta functions, three spatial dimensions, unbounded domains, and rapid (exponential) nonlinearity. However, these adaptive techniques have shown substantial improvement in solution time over conventional uniform‐mesh finite difference methods. One important aspect of the adaptive multilevel finite element method is the robust a posteriori error estimators necessary to drive the adaptive refinement routines. This article discusses the choice of solvent accessibility for a posteriori error estimation of PBE solutions and the implementation of such routines in the “Adaptive Poisson–Boltzmann Solver” (APBS) software package based on the “Manifold Code” (MC) libraries. Results are shown for the application of this method to several biomolecular systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1343–1352, 2000     

The effects of laser field fluctuations on multiphoton excitation of a multilevel system

In this paper we analyze the effects of the fluctuations of laser amplitude on the multiphoton excitation of a sparse multilevel molecular system. It is found that contrary to the excitation by a laser with phase fluctuations, the stochastic contribution of the amplitude fluctuations is non-diagonal and scrambles the off-diagonal elements of the general molecular density matrix, resulting in temporal oscillations of these terms. The chaotic field model for the laser amplitude cannot force the applicability of the kinetic master equation for a general multilevel system. It is found that, for the two-level system driven by a chaotic field model laser, The stochastic interlevel rate dumps the oscillatory behaviour of the molecular populations, validating the master equation by T₁-type effects.     

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

修正的格子空间的密度泛函理论在狭缝中的应用

对描述单原子分子溶液在狭缝中的吸附现象的格子空间的密度泛函理论 (LDFT, lattice density functional theory)进行了修正, 在系统Helmholtz函数的推导中引入了平均场近似校正和Gibbs-Helmholtz方程. 对比Monte Carlo (MC)模拟结果, 发现LDFT理论对吸附分子在狭缝中的吸附浓度分布的预测与模拟数据有较大的偏差, 而修正模型的结果与模拟数据吻合较好 .随着体相浓度的变化,分子在狭缝中具有多级吸附行为, 具体表现为在特定体相浓度区, 对相同的体相浓度,狭缝中同时存在不同的分子浓度分布, 而在Gibbs等温线上可以明显看出多级吸附的性质. 对比修正前后的结果发现,两者均可以预测多级吸附行为, 但仍存在着较大的差异.     

Exact semiclassical solution for the time evolution of a quantum-mechanical system in a circularly polarized monochromatic driving field

A closed-form exact solution is presented for the time evolution operator of a nonrelativistic hydrogen atom driven by a circularly polarized monochromatic light beam. The solution has the form U(t, 0) = exp(?itF)exp(?itG), where F and G are time independent operators. All temporal effects of the oscillating field are included. Extension to other systems is easily made. A generalization of the rotating wave approximation to multilevel systems is also presented.     

Microscopic Studies of Diffusion and Segregation Processes in Heavily Loaded Tribosystems

Russian Journal of Applied Chemistry - The construction of a wearing-process model is considered. This model should take into account not only the complex multilevel organization of the process,...     

Multicoefficient extrapolated density functional theory studies of pi...pi interactions: the benzene dimer

We report tests of new (2005) and established (1999-2003) multilevel methods against essentially converged benchmark results for nonbonded interactions in benzene dimers. We found that the newly developed multicoefficient extrapolated density functional theory (DFT) methods (which combine DFT with correlated wave function methods) give better performance than multilevel methods such as G3SX, G3SX(MP3), and CBS-QB3 that are based purely on wave function theory (WFT); furthermore, they have a lower computational cost. We conclude that our empirical approach for combining WFT methods with DFT methods is a very efficient and effective way for describing not only covalent interactions (as shown previously) but also nonbonded interactions.