Embedding Function Research Articles

Structure and energetics of nickel, copper, and gold clusters

The most stable structures of CuN, NiN, and AuN clusters with 2≤N≤60 have been determined using a combination of the embedded-atom (EAM), the quasi-Newton, and our own Aufbau/Abbau methods for the calculation of the total energy for a given structure, the structures of the local total-energy minima, and the structure of the global total-energy minimum, respectively. We have employed two well-known versions of the EAM: (1) the ‘bulk’ version of Daw, Baskes, and Foiles and (2) the Voter-Chen version which takes into account also properties of the dimer in the parameterization. The lower-energy structures (also for the smallest) of CuN and NiN clusters (i.e., structural details as well as symmetry) obtained with the two versions are very similar. Thus, our study supports an universality of the bulk embedding functions for copper and nickel. But for gold clusters the differences between structures calculated with the two different versions of the EAM are significant, even for larger clusters.

Hamiltonian dynamics of extended objects

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler–Lagrange equations.

Fuzzy optimization problemsbased on the embedding theorem and possibility and necessity measures

The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem based on the possibility and necessity measures by solving a biobjective optimization problem. This biobjective optimization problem is obtained by applying the embedding function to the original fuzzy optimization problem. We then also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed to be fuzzy numbers). Under a setting of core value of fuzzy number, we show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also a 1-optimal solution of the original fuzzy optimization problem.

An (α ,β)-Optimal solution concept in Fuzzy Optimization problems

We propose an (α,β)-optimal solution concept of fuzzy optimization problem based on the possibility and necessity measures. It is well known that the set of all fuzzy numbers can be embedded into a Banach space isometrically and isomorphically. Inspired by this embedding theorem, we can transform the fuzzy optimization problem into a biobjective programming problem by applying the embedding function to the original fuzzy optimization problem. Then the (α,β)-optimal solutions of fuzzy optimization problem can be obtained by solving its corresponding biobjective programming problem. We also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed as fuzzy numbers). Under a setting of core value of fuzzy numbers, we provide the Karush–Kuhn–Tucker optimality conditions and show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also a (1,1)-optimal solution of the original fuzzy optimization problem.

Development of Modified Embedded Atom Method for Alkali Metals

The modified embedded atom method (MEAM) can describe the physical properties of bulk systems for a wide range of advanced engineering materials. However, the MEAM is found to return negative surface energy for Li(100), Li(110) and Li(111), if the relaxation of atomic positions on the surface is taken into account. In order to solve this problem, a new scheme of MEAM for lithium has been developed, by modifying the expression of embedding function. In this work, the new scheme is also applied to the other alkali metals, and the parameter sets of MEAM have been determined by fitting to not only bulk properties but also some non-bulk properties. The new MEAM potentials for alkali metals have been applied to calculate the elastic stiffness of crystal, the vacancy formation energy, the surface energies for low index crystal faces and the bond length and the binding energy for dimer. The results have been compared with experimental values.

Encoding types in ML-like languages

This article presents several general approaches to programming with type-indexed families of values within a Hindley–Milner type system. A type-indexed family of values is a function that maps a family of types to a family of values. The function performs a case analysis on the input types and returns values of possibly different types. Such a case analysis on types seems to be prohibited by the Hindley–Milner type system. Our approaches solve the problem by using type encodings. The compile-time types of the type encodings reflect the types themselves, thereby making the approaches type-safe, in the sense that the underlying type system statically prevents any mismatch between the input type and the function arguments that depend on this type. A type encoding could be either value-dependent, meaning that the type encoding is tied to a specific type-indexed family, or value-independent, meaning that the type encoding can be shared by various type-indexed families. Our first approach is value-dependent: we simply interpret a type as its corresponding value. Our second approach provides value-independent type encodings through embedding and projection functions; they are universal type interpretations, in that they can be used to compute other type interpretations. We also present an alternative approach to value-independent type encodings, using higher-order functors. We demonstrate our techniques through applications such as C printf-like formatting, type-directed partial evaluation, and subtype coercions.

Development of a modified embedded atom method for bcc transition metals

A new scheme of the modified embedded atom method (MEAM) is developed by modifyingthe analytic form of the embedding function. The new MEAM parameters for Mo, W, V,Nb, Ta and Fe have been determined by relating them to not only bulk properties but alsosome non-bulk properties. The new scheme was applied to calculate the elastic stiffnessof the crystal, the vacancy formation energy, the lattice stability, the surfaceenergies for low-index crystal faces and the bond length and the binding energyfor the dimer. The results give a fairly good agreement with the experimentaldata.

A note on Hamilton–Jacobi formalism and D-brane effective actions

We first review the canonical formalism with general space-like hypersurfaces developed by Dirac by rederiving the Hamilton–Jacobi equations which are satisfied by on-shell actions defined on such hypersurfaces. We compare the case of gravitational systems with that of the flat space. Next, we remark as a supplement to our previous results that the effective actions of D-brane and M-brane given by arbitrary embedding functions are on-shell actions of supergravities.

Solving variational problems and partial differential equations mapping into general target manifolds

A framework for solving variational problems and partial differential equations that define maps onto a given generic manifold is introduced in this paper. We discuss the framework for arbitrary target manifolds, while the domain manifold problem was addressed in [J. Comput. Phys. 174(2) (2001) 759]. The key idea is to implicitly represent the target manifold as the level-set of a higher dimensional function, and then implement the equations in the Cartesian coordinate system where this embedding function is defined. In the case of variational problems, we restrict the search of the minimizing map to the class of maps whose target is the level-set of interest. In the case of partial differential equations, we re-write all the equation’s geometric characteristics with respect to the embedding function. We then obtain a set of equations that, while defined on the whole Euclidean space, are intrinsic to the implicitly defined target manifold and map into it. This permits the use of classical numerical techniques in Cartesian grids, regardless of the geometry of the target manifold. The extension to open surfaces and submanifolds is addressed in this paper as well. In the latter case, the submanifold is defined as the intersection of two higher dimensional hypersurfaces, and all the computations are restricted to this intersection. Examples of the applications of the framework here described include harmonic maps in liquid crystals, where the target manifold is a hypersphere; probability maps, where the target manifold is a hyperplane; chroma enhancement; texture mapping; and general geometric mapping between high dimensional manifolds.

Generalized patchwork algorithm for image watermarking

This paper presents the generalized patchwork algorithm (GPA), which is an extension of the modified patchwork algorithm (MPA). The MPA embeds watermarks additively and changes the mean of the pixels accordingly. In this paper, we take multiplicative watermarks into consideration where the GPA can change the variance of pixels. The GPA combines both additive watermarks and multiplicative watermarks. The embedding functions of the GPA determine embedding parameters adaptively according to the host signals. Detection functions also determine thresholds adaptively. Embedding and detection functions based on the test of statistical hypotheses are presented in this paper. Simulation results show the effectiveness of the GPA. The proposed algorithm is sufficiently robust against various signal processing operations, especially against compression attacks.

Development of modified embedded atom method for a bcc metal: lithium

A new scheme of modified embedded atom method (MEAM) is proposed in this paper. The analytic form of the embedding function is modified. All the parameters of MEAM have been reset by relating them with bulk properties and some non-bulk properties, for example, the bond length of a dimer and the change of surface interlayer distance. The new scheme has been applied to calculate the elastic stiffness of crystal, the vacancy formation energy and some properties of non-bulk systems such as the surface energies for low index crystal faces, the bond length and the binding energy for a dimer. The results are compared with the experimental data and get a fairly good agreement.

Scalar costa scheme for information embedding

Research on information embedding, particularly information hiding techniques, has received considerable attention within the last years due to its potential application in multimedia security. Digital watermarking, which is an information hiding technique where the embedded information is robust against malicious or accidental attacks, might offer new possibilities to enforce the copyrights of multimedia data. In this paper, the specific case of information embedding into independent identically distributed (IID) data and attacks by additive white Gaussian noise (AWGN) is considered. The original data is not available to the decoder. For Gaussian data, in 1983, Costa proposed a scheme that theoretically achieves the capacity of this communication scenario. However, Costa's scheme is not practical. Thus, several research groups have proposed suboptimal practical communication schemes based on Costa's idea. The goal of this paper is to give a complete performance analysis of the scalar Costa scheme (SCS), which is a suboptimal technique using scalar embedding and reception functions. Information theoretic bounds and simulation results with state-of-the-art coding techniques are compared. Further, reception after amplitude scaling attacks and the invertibility of SCS embedding are investigated.

An embedded atom method interatomic potential for the Cu–Pb system

A simple procedure is used to formulate a Cu–Pb pair interaction function within the embedded atom (EAM) method framework. Embedding, density and pair functions for pure Cu and pure Pb are taken from previously published EAM studies. Optimization of the Cu–Pb potential was achieved by comparing with experiment the computed heats of mixing for Cu–Pb liquid alloys and the equilibrium phase diagram, the latter being determined via a thermodynamic integration technique. The topology of the temperature-composition phase diagram computed with this EAM potential is consistent with experiment and features a liquid–liquid miscibility gap, low solubility of Pb in solid Cu and a monotectic reaction at approximately 1012 K.

第一原理計算による高圧分子固体の探究‐高圧固体アルゴンの多原子斥力相互作用

The many-atom character of interactions in fcc solid argon at high pressures is discussed. The cubic elastic constants and violation of the Cauchy relationship as a function of hydrostatic pressure, which have been measured recently by Shimizu et al., are shown to be very well reproduced by a full-potential and all-electron total energy scheme with a generalized gradient approximation for the exchange-correlation energy functional. It is shown that an essential many-atom feature can most simply be introduced through some appropriate embedding or environment-dependent functions brought into pair-wise interactions.

A flexible sigmoid function of determinate growth.

A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.

FlexWare: a retargetable, embedded-software development environment

Effective embedded software development tools are essential to better exploit the inherent capabilities of these processors. We developed the FlexWare embedded software development environment in response to this need, focusing essentially on the performance and retargetability of our tools. Our benchmarks demonstrate that, despite the wide range of processors we cover, we have achieved state-of-the-art embedded software-tool performance and functionality. Moreover, we demonstrate their wide range of retargetability, ranging from simple microcontrollers to complex multimedia DSPs and network processors.

Relationship between the modified embedded-atom method and Stillinger-Weber potentials in calculating the structure of silicon

We show that the Stillinger-Weber (SW) potential is a special case of the modified embedded-atom method (MEAM) potential, by deriving the appropriate functional forms and parameter values for the MEAM potential. The electron density and pair potential functions have physically plausible forms. The embedding function is quadratic in the electron density and yields an antibonding contribution under all circumstances. Using these results SW silicon can be conveniently extended to silicon-metal systems within one theoretical framework and one computational scheme. The properties of SW silicon and silicon modeled by the native MEAM representation are compared.

Variational Problems and Partial Differential Equations on Implicit Surfaces

A novel framework for solving variational problems and partial differential equations for scalar and vector-valued data defined on surfaces is introduced in this paper. The key idea is to implicitly represent the surface as the level set of a higher dimensional function and to solve the surface equations in a fixed Cartesian coordinate system using this new embedding function. The equations are then both intrinsic to the surface and defined in the embedding space. This approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces, as is commonly done in the literature. We describe the framework and present examples in computer graphics and image processing applications, including texture synthesis, flow field visualization, and image and vector field intrinsic regularization for data defined on 3D surfaces.

Surface embedded atom model of the electrolyte-metal interface

We develop a semiempirical interatomic potential model based on the surface embedded atom method (SEAM) for simulating the metal-electrolyte interface in the presence of excess surface charge on the metal electrode surface in an electrochemical cell. We take the excess charge into account by modifying the electron density in the embedding function of the SEAM potential. We calculate total and surface energies and the surface stress as functions of the cell voltage [relative to the potential of zero charge (PZC)] for gold electrodes and compare with reported measurements. The values of the two parameters that occur in our model are fit to the measured work function and capacitance of the Au(111) surface. The parameter corresponding to the height of the surface layer is in close agreement with that obtained from density-functional theory calculations. A similar fit is also carried out for silver electrodes. The calculated values of the PZC for low index faces of gold and silver follow the trend observed experimentally. Our results suggest that the SEAM potentials can reasonably describe the physics of the metal-electrolyte interface.

Component-based software as a framework for concurrent design of programs and platforms — an industrial kitchen appliance embedded system

Designs of hardware, mechanics and software for a new mechatronic system are to be performed concurrently in order to have a new product in the market in the shortest possible time. Traditionally, major hardware blocks need to be designed and built first. They represent a platform for software writing and testing. A software design concept that enables a parallel design of hardware, mechanics and software is presented. The concept implies creation of a framework for a component-based software design first. Then, a component-based design is performed. At software design time, software components yield embedded system functionality, and they also model hardware and mechanics functionality. As hardware and mechanical parts are built, they are integrated with functionality components, already designed, written and verified. The critical software design task is splitting the embedded software functionality and hardware model into self-contained, self-sufficient components, easy to manage simple interfaces. The concept is demonstrated by a case of designing software for a potato fryer. Software components are designed to be transportable to other industrial kitchen appliances (bain-marie, tilting pan, range) via parameter adjustments only. In the case study of a potato fryer, 90% of microcontroller code was implemented and verified as software components in a C++ Builder environment running on a personal computer at the same time as hardware and fryer mechanical parts were built. 10% of code was written and final parameter adjustments were performed on a simple microcontroller development system.