Journal articles: 'Approximation du potentiel'

1

Koumantiga, Dabitora. "Ecotourisme et aires protégées: L’histoire, un potentiel latent pour le complexe OKM (Togo, Afrique)." PASOS. Revista de Turismo y Patrimonio Cultural 19, no. 2 (2021): 223–38. http://dx.doi.org/10.25145/j.pasos.2021.19.015.

Full text

Abstract:

In Mexico, there are 194 archaeological zones open to the public under the custody of the National Institute for Anthropology and History. However, there are also many other sites that operate outside the federal management model and the current legal framework. These are called “limbos” here and are clas‑ sified by who administers them and the land ownership regime. Through the review of three cases spread over Mexico, a first approximation of their key problems and shared dynamics is offered that factors in legal, bureaucratic and socioeconomic aspects that underlie the unauthorized use of archaeological heritage. It is concluded that they are “in limbo “mainly due to ambiguities in the legislation and loopholes that have been exploited by stakeholders to allow them to use of these ruins as a tourist attraction.

APA, Harvard, Vancouver, ISO, and other styles

2

Payne, Joshua L., and Margaret J. Eppstein. "Pair Approximations of Takeover Dynamics in Regular Population Structures." Evolutionary Computation 17, no. 2 (June 2009): 203–29. http://dx.doi.org/10.1162/evco.2009.17.2.203.

Full text

Abstract:

In complex adaptive systems, the topological properties of the interaction network are strong governing influences on the rate of flow of information throughout the system. For example, in epidemiological models, the structure of the underlying contact network has a pronounced impact on the rate of spread of infectious disease throughout a population. Similarly, in evolutionary systems, the topology of potential mating interactions (i.e., population structure) affects the rate of flow of genetic information and therefore affects selective pressure. One commonly employed method for quantifying selective pressure in evolutionary algorithms is through the analysis of the dynamics with which a single favorable mutation spreads throughout the population (a.k.a. takeover time analysis). While models of takeover dynamics have been previously derived for several specific regular population structures, these models lack generality. In contrast, so-called pair approximations have been touted as a general technique for rapidly approximating the flow of information in spatially structured populations with a constant (or nearly constant) degree of nodal connectivities, such as in epidemiological and ecological studies. In this work, we reformulate takeover time analysis in terms of the well-known Susceptible-Infectious-Susceptible model of disease spread and adapt the pair approximation for takeover dynamics. Our results show that the pair approximation, as originally formulated, is insufficient for approximating pre-equibilibrium dynamics, since it does not properly account for the interaction between the size and shape of the local neighborhood and the population size. After parameterizing the pair approximation to account for these influences, we demonstrate that the resulting pair approximation can serve as a general and rapid approximator for takeover dynamics on a variety of spatially-explicit regular interaction topologies with varying population sizes and varying uptake and reversion probabilities. Strengths, limitations, and potential applications of the pair approximation to evolutionary computation are discussed.

APA, Harvard, Vancouver, ISO, and other styles

3

Makhlaichuk, P. V., M. P. Malomuzh, and I. V. Zhyganiuk. "Potential in the Multipole Approximation." Ukrainian Journal of Physics 58, no. 3 (March 2013): 278–88. http://dx.doi.org/10.15407/ujpe58.03.0278.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Hao, Qi, and Alexey Stovas. "Analytic calculation of phase and group velocities of P-waves in orthorhombic media." GEOPHYSICS 81, no. 3 (May 2016): C79—C97. http://dx.doi.org/10.1190/geo2015-0156.1.

Full text

Abstract:

We have developed an approximate method to calculate the P-wave phase and group velocities for orthorhombic media. Two forms of analytic approximations for P-wave velocities in orthorhombic media were built by analogy with the five-parameter moveout approximation and the four-parameter velocity approximation for transversely isotropic media, respectively. They are called the generalized moveout approximation (GMA)-type approximation and the Fomel approximation, respectively. We have developed approximations for elastic and acoustic orthorhombic media. We have characterized the elastic orthorhombic media in Voigt notation, and we can describe the acoustic orthorhombic media by introducing the modified Alkhalifah’s notation. Our numerical evaluations indicate that the GMA-type and Fomel approximations are accurate for elastic and acoustic orthorhombic media with strong anisotropy, and the GMA-type approximation is comparable with the approximation recently proposed by Sripanich and Fomel. Potential applications of the proposed approximations include forward modeling and migration based on the dispersion relation and the forward traveltime calculation for seismic tomography.

APA, Harvard, Vancouver, ISO, and other styles

5

DELLAR, PAUL J. "Variations on a beta-plane: derivation of non-traditional beta-plane equations from Hamilton's principle on a sphere." Journal of Fluid Mechanics 674 (March 14, 2011): 174–95. http://dx.doi.org/10.1017/s0022112010006464.

Full text

Abstract:

Starting from Hamilton's principle on a rotating sphere, we derive a series of successively more accurate β-plane approximations. These are Cartesian approximations to motion in spherical geometry that capture the change with latitude of the angle between the rotation vector and the local vertical. Being derived using Hamilton's principle, the different β-plane approximations each conserve energy, angular momentum and potential vorticity. They differ in their treatments of the locally horizontal component of the rotation vector, the component that is usually neglected under the traditional approximation. In particular, we derive an extended set of β-plane equations in which the locally vertical and locally horizontal components of the rotation vector both vary linearly with latitude. This was previously thought to violate conservation of angular momentum and potential vorticity. We show that the difficulty in maintaining these conservation laws arises from the need to express the rotation vector as the curl of a vector potential while approximating the true spherical metric by a flat Cartesian metric. Finally, we derive depth-averaged equations on our extended β-plane with topography, and show that they coincide with the extended non-traditional shallow-water equations previously derived in Cartesian geometry.

APA, Harvard, Vancouver, ISO, and other styles

6

STOJANOVIĆ, MIRJANA. "PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA." Communications in Contemporary Mathematics 08, no. 04 (August 2006): 433–52. http://dx.doi.org/10.1142/s0219199706002180.

Full text

Abstract:

We consider linear Schrödinger equation perturbed by delta distribution with singular potential and the initial data. Due to the singularities appearing in the equation, we introduce two kinds of approximations: the parameter's approximation for potential and the initial data given by mollifiers of different growth and the approximation for the Green function for Schrödinger equation with regularized derivatives. These approximations reduce the perturbed Schrödinger equation to the family of singular integral equations. We prove the existence-uniqueness theorems in Colombeau space [Formula: see text], 1 ≤ p,q ≤ ∞, employing novel stability estimates (w.r.) to singular perturbations for ε → 0, which imply the statements in the framework of Colombeau generalized functions. In particular, we prove the existence-uniqueness result in [Formula: see text] and [Formula: see text] algebra of Colombeau.

APA, Harvard, Vancouver, ISO, and other styles

7

Evans, Richard B. "The Convergence of the Legendre–Galerkin Spectral Method for Constructing Atmospheric Acoustic Normal Modes." Journal of Theoretical and Computational Acoustics 28, no. 03 (September 2020): 2050002. http://dx.doi.org/10.1142/s2591728520500024.

Full text

Abstract:

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.

APA, Harvard, Vancouver, ISO, and other styles

8

Thien, Austen, Christopher Saldana, and Thomas Kurfess. "Surface Qualification Toolpath Optimization for Hybrid Manufacturing." Journal of Manufacturing and Materials Processing 5, no. 3 (August 27, 2021): 94. http://dx.doi.org/10.3390/jmmp5030094.

Full text

Abstract:

Hybrid manufacturing machine tools have great potential to revolutionize manufacturing by combining both additive manufacturing (AM) and subtractive manufacturing (SM) processes on the same machine tool. A prominent issue that can occur when going from AM to SM is that the SM process toolpath does not account for geometric discrepancies caused by the previous AM step, which leads to increased production times and tool wear, particularly when wire-based directed energy deposition (DED) is used as the AM process. This work discusses a methodology for approximating a part’s surface topology using on-machine contact probing and formulating an optimized SM toolpath using the surface topology approximation. Three different geometric surface approximations were used: triangular, trapezoidal, and a hybrid of both. SM toolpaths were created using each geometric approximation and assessed according to three objectives: reducing total machining time, reducing surface roughness, and reducing cutting force. Different prioritization scenarios of the optimization goals were also investigated. The optimal surface approximation that yielded the most improvement in the optimization was determined to be the hybrid surface topology approximation. Furthermore, it was shown that when the machining time or cutting force optimization goals were prioritized, there was little improvement in the other optimization goals.

APA, Harvard, Vancouver, ISO, and other styles

9

JAVADIMANESH, E., H. HASSANABADI, A. A. RAJABI, H. RAHIMOV, and S. ZARRINKAMAR. "ALPHA-DECAY HALF-LIVES OF DEFORMED NUCLEI BY AN ANGLE-DEPENDENT POTENTIAL." Modern Physics Letters A 27, no. 38 (December 2, 2012): 1250226. http://dx.doi.org/10.1142/s0217732312502264.

Full text

Abstract:

The half-lives of deformed nuclei are reported. We consider an angle-dependent potential which yields multipole approximations. We see that the results are in better agreement with the experimental data when the multipole approximation is solely considered for the daughter nuclei.

APA, Harvard, Vancouver, ISO, and other styles

10

Tuan, Hoang Anh. "The Equivalence of CPA and Hubbard-III-I Approximation in the Two-Band Hubbard Model." Modern Physics Letters B 11, no. 18 (August 10, 1997): 779–84. http://dx.doi.org/10.1142/s0217984997000967.

Full text

Abstract:

We study a two-band Hubbard model using the Coherent Potential Approximation (CPA) and equation of motion decoupling scheme with scattering correction (Hubbard-III-I approximation). We show that above two approximations are completely equivalent to each other for the Periodic Anderson Model (PAM) as well as for the Self-doped Mott System (SMS).

APA, Harvard, Vancouver, ISO, and other styles

11

CHEN, ZHAO-YOU, MIN LI, and CHUN-SHENG JIA. "APPROXIMATE ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE MANNING–ROSEN POTENTIAL MODEL." Modern Physics Letters A 24, no. 23 (July 30, 2009): 1863–74. http://dx.doi.org/10.1142/s0217732309030345.

Full text

Abstract:

By approximating the centrifugal term in terms of a new approximation scheme, we solve the Schrödinger equation with the arbitrary angular momentum for the Manning–Rosen potential. The bound state energy eigenvalues and the unnormalized radial wave functions have been approximately obtained by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our approximate analytical results are in better agreement with those obtained by using the numerical integration procedure than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

APA, Harvard, Vancouver, ISO, and other styles

12

McCarthy, IE. "The Electron - Atom Ionisation Problem." Australian Journal of Physics 49, no. 2 (1996): 219. http://dx.doi.org/10.1071/ph960219.

Full text

Abstract:

Methods of calculating electron–atom ionisation as a three-body problem with Coulomb boundary conditions are considered. In the absence of a fully-valid computational method for a time-independent experiment the approximation is made that the incident electron experiences a screened potential. Approximations involving a final state that obeys the three-body Coulomb boundary condition are compared with the distorted-wave Born approximation and the convergent close-coupling method.

APA, Harvard, Vancouver, ISO, and other styles

13

Noblesse, Francis. "Numerical Study of a Slender-Ship Theory of Wave Resistance." Journal of Ship Research 29, no. 02 (June 1, 1985): 81–93. http://dx.doi.org/10.5957/jsr.1985.29.2.81.

Full text

Abstract:

This study is a continuation of the previous numerical study by Chen and Noblesse [1]2 of the slender-ship theory of wave resistance presented in Noblesse [2]. Results of systematic calculations of wave resistance are presented for three simple sharp-and round-ended strut-like hull forms having beam/length and draft/length ratios equal to 0.15 and 0.075, respectively. Numerical results are presented for the first order slender-ship approximation and for seven closely related wave-resistance approximations. The nondimensional wave-resistance values associated with these eight approximations are plotted versus the Froude number in the range 1 ≥ F ≥ 0.18. The Kochin wave-energy function corresponding to four approximations is also depicted for three Froude-number values. The wave potential is shown to have more pronounced effects upon the wave resistance, causing large phase shifts in particular, than the nonoscillatory near-field potential. A simple analytical approximation to the near-field term in the Green function is proposed. Finally, theoretical predictions are compared with experimental data for the Sharma strut and the Wigley hull.

APA, Harvard, Vancouver, ISO, and other styles

14

BOKANOWSKI, OLIVIER, and NORBERT J. MAUSER. "LOCAL APPROXIMATION FOR THE HARTREE–FOCK EXCHANGE POTENTIAL: A DEFORMATION APPROACH." Mathematical Models and Methods in Applied Sciences 09, no. 06 (August 1999): 941–61. http://dx.doi.org/10.1142/s0218202599000439.

Full text

Abstract:

We present a method for deriving local approximations of the exchange-term in the Hartree–Fock equation for a system of fermions interacting with a Coulomb-force. Within our model, we give a justification of the Slater-approximation where the exchange-term is replaced by the third root of the local density. Our approach is based on deformations, i.e. local scaling transformations of a constant density, combined with the "high density limit" of infinite number of particles.

APA, Harvard, Vancouver, ISO, and other styles

15

Rocha, Cesar B., William R. Young, and Ian Grooms. "On Galerkin Approximations of the Surface Active Quasigeostrophic Equations." Journal of Physical Oceanography 46, no. 1 (January 2016): 125–39. http://dx.doi.org/10.1175/jpo-d-15-0073.1.

Full text

Abstract:

AbstractThis study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

APA, Harvard, Vancouver, ISO, and other styles

16

Abadi, Miguel, Vitor Amorim, and Sandro Gallo. "Potential Well in Poincaré Recurrence." Entropy 23, no. 3 (March 23, 2021): 379. http://dx.doi.org/10.3390/e23030379.

Full text

Abstract:

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

APA, Harvard, Vancouver, ISO, and other styles

17

James, Guillaume. "Travelling breathers and solitary waves in strongly nonlinear lattices." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2127 (July 23, 2018): 20170138. http://dx.doi.org/10.1098/rsta.2017.0138.

Full text

Abstract:

We study the existence of travelling breathers and solitary waves in the discrete p -Schrödinger (DpS) equation. This model consists of a one-dimensional discrete nonlinear Schrödinger (NLS) equation with strongly nonlinear inter-site coupling (a discrete p -Laplacian). The DpS equation describes the slow modulation in time of small amplitude oscillations in different types of nonlinear lattices, where linear oscillators are coupled to nearest-neighbours by strong nonlinearities. Such systems include granular chains made of discrete elements interacting through a Hertzian potential ( p = 5/2 for contacting spheres), with additional local potentials or resonators inducing local oscillations. We formally derive three amplitude PDEs from the DpS equation when the exponent of nonlinearity is close to (and above) unity, i.e. for p lying slightly above 2. Each model admits localized solutions approximating travelling breather solutions of the DpS equation. One model is the logarithmic NLS equation which admits Gaussian solutions, and the other is fully nonlinear degenerate NLS equations with compacton solutions. We compare these analytical approximations to travelling breather solutions computed numerically by an iterative method, and check the convergence of the approximations when . An extensive numerical exploration of travelling breather profiles for p = 5/2 suggests that these solutions are generally superposed on small amplitude non-vanishing oscillatory tails, except for particular parameter values where they become close to strictly localized solitary waves. In a vibro-impact limit where the parameter p becomes large, we compute an analytical approximation of solitary wave solutions of the DpS equation. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

APA, Harvard, Vancouver, ISO, and other styles

18

Li, Bao-Fei, Tao Zhu, and Anzhong Wang. "Langer Modification, Quantization Condition and Barrier Penetration in Quantum Mechanics." Universe 6, no. 7 (June 30, 2020): 90. http://dx.doi.org/10.3390/universe6070090.

Full text

Abstract:

The WKB approximation plays an essential role in the development of quantum mechanics and various important results have been obtained from it. In this paper, we introduce another method, the so-called uniform asymptotic approximations, which is an analytical approximation method to calculate the wave functions of the Schrödinger-like equations, and it is applicable to various problems, including cases with poles (singularities) and multiple turning points. A distinguished feature of the method is that in each order of the approximations the upper bounds of the errors are given explicitly. By properly choosing the freedom introduced in the method, the errors can be minimized, which significantly improves the accuracy of the calculations. A byproduct of the method is to provide a very clear explanation of the Langer modification encountered in the studies of the hydrogen atom and harmonic oscillator. To further test our method, we calculate (analytically) the wave functions for several exactly solvable potentials of the Schrödinger equation, and then obtain the transmission coefficients of particles over potential barriers, as well as the quantization conditions for bound states. We find that such obtained results agree with the exact ones extremely well. Possible applications of the method to other fields are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

19

Falaye, B. J., K. J. Oyewumi, T. T. Ibrahim, M. A. Punyasena, and C. A. Onate. "Bound state solutions of the Manning–Rosen potential." Canadian Journal of Physics 91, no. 1 (January 2013): 98–104. http://dx.doi.org/10.1139/cjp-2012-0330.

Full text

Abstract:

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the ℓ-wave solutions of the Schrödinger equation with the Manning–Rosen potential. The energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers n and ℓ for some diatomic molecules (HCl, CH, LiH, and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulthén potential case are also presented.

APA, Harvard, Vancouver, ISO, and other styles

20

Koch, Othmar. "Convergence of exponential Lawson-multistep methods for the MCTDHF equations." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 6 (November 2019): 2109–19. http://dx.doi.org/10.1051/m2an/2019033.

Full text

Abstract:

We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.

APA, Harvard, Vancouver, ISO, and other styles

21

Kachanov, M., I. Tsukrov, and B. Shafiro. "Effective Moduli of Solids With Cavities of Various Shapes." Applied Mechanics Reviews 47, no. 1S (January 1, 1994): S151—S174. http://dx.doi.org/10.1115/1.3122810.

Full text

Abstract:

Effective elastic properties of solids with cavities of various shapes are derived in two approximations: the approximation of non-interacting cavities and the approximation of the average stress field (Mori-Tanaka’s scheme); the latter appears to be appropriate when mutual positions of defects are random. We construct the elastic potential of a solid with cavities. Such an approach covers, in a unified way, cavities of various shapes and any mixture of them. No degeneracies (or a need in a special limiting procedure) arise when cavities shrink to cracks. It also provides a unified description of both isotropic and anisotropic effective properties and recovers results available in the literature for special cases. Elastic potentials dictate the choice of proper parameters of cavity density. These parameters depend on defect shapes. Even in the case of random orientations, the isotropic overall properties cannot be characterized in terms of porosity alone; for elliptical holes, for example, a second parameter - “eccentricity” - is needed.

APA, Harvard, Vancouver, ISO, and other styles

22

MESSUD, J., P. M. DINH, E. SURAUD, and P. G. REINHARD. "ON THE "GENERALIZED SLATER" APPROXIMATION." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 4087–95. http://dx.doi.org/10.1142/s0217979209063274.

Full text

Abstract:

We work within the Density Functional Theory (DFT), in the Local Density Approximation (LDA) with Self Interaction Correction (SIC). We show that, thanks to a formulation which employs two different sets of orbitals, the equations can be written in the form of eigenvalues equations, leading to single electron interpretation. However, the resulting hamiltonian is non-local. We propose to find it's best local approximation within using the Optimized Effective Potential (OEP) method. The resulting approximate theory is denominated "Generalized Slater". We show that this new scheme cures the pathologies of the standard SIC-Slater or SIC-KLI approximations.

APA, Harvard, Vancouver, ISO, and other styles

23

Narimani, M., and Z. Nourbakhsh. "Topological band order, structural, electronic and optical properties of XPdBi (X = Lu, Sc) compounds." Modern Physics Letters B 30, no. 14 (May 29, 2016): 1650159. http://dx.doi.org/10.1142/s0217984916501591.

Full text

Abstract:

In this paper, the structural, electronic and optical properties of LuPdBi and ScPdBi compounds are investigated using the density functional theory by WIEN2K package within the generalized gradient approximation, local density approximation, Engel–Vosco generalized gradient approximations and modified Becke–Johnson potential approaches. The topological phases and band orders of these compounds are studied. The effect of pressure on band inversion strength, electron density of states and the linear coefficient of the electronic specific heat of these compounds is investigated. Furthermore, the effect of pressure on real and imaginary parts of dielectric function, absorption and reflectivity coefficients of these compounds is studied.

APA, Harvard, Vancouver, ISO, and other styles

24

Le, Chien Hoang, Cuong Cong Do, Phuc Hoang Nguyen, and Khoa Tien Dao. "Study of the nuclear medium by 12C + 12C elastic scattering analysis at low energy region." Science and Technology Development Journal - Natural Sciences 1, T2 (June 30, 2017): 75–82. http://dx.doi.org/10.32508/stdjns.v1it2.454.

Full text

Abstract:

The nuclear medium is investigated by studying the 12C + 12C elastic scattering at the low energies in the framework of optical model (OM) potential. Both frozen and adiabatic density approximations are used for the description of the nuclear medium during the colliding process. In the OM calculation, the double folding procedure using the realistic CDM3Y3 effective nucleon-nucleon (NN) interactions and the wave functions of colliding nuclei is employed to describe the nucleus-nucleus potential at low energy region below 10 MeV per nucleon. The obtained results from the elastic scattering analyses show that the adiabatic density approximation is more reasonable than the frozen density approximation to describe the overlapping density (the so-called nuclear medium) for the 12C + 12C system at low energy region.

APA, Harvard, Vancouver, ISO, and other styles

25

Schütze, Oliver, Marco Laumanns, Emilia Tantar, Carlos A. Coello Coello, and El-Ghazali Talbi. "Computing Gap Free Pareto Front Approximations with Stochastic Search Algorithms." Evolutionary Computation 18, no. 1 (March 2010): 65–96. http://dx.doi.org/10.1162/evco.2010.18.1.18103.

Full text

Abstract:

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of ɛ-dominance. Though bounds on the quality of the limit approximation—which are entirely determined by the archiving strategy and the value of ɛ—have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a ∈ A, is “large.” Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy—multi-objective continuation methods—by showing that the concept of ɛ-dominance can be integrated into this approach in a suitable way.

APA, Harvard, Vancouver, ISO, and other styles

26

Bakhshaii, Atoossa, and Roland Stull. "Saturated Pseudoadiabats—A Noniterative Approximation." Journal of Applied Meteorology and Climatology 52, no. 1 (January 2013): 5–15. http://dx.doi.org/10.1175/jamc-d-12-062.1.

Full text

Abstract:

AbstractTwo noniterative approximations are presented for saturated pseudoadiabats (also known as moist adiabats). One approximation determines which moist adiabat passes through a point of known pressure and temperature, such as through the lifting condensation level on a skew T or tephigram. The other approximation determines the air temperature at any pressure along a known moist adiabat, such as the final temperature of a rising cloudy air parcel. The method used to create these statistical regressions is a relatively new variant of genetic programming called gene-expression programming. The correlation coefficient between the resulting noniterative approximations and the iterated data such as plotted on thermodynamic diagrams is over 99.97%. The mean absolute error is 0.28°C, and the root mean square error is 0.44 within a thermodynamic domain bounded by −30° < θw ≤ 40°C, P > 20 kPa, and −60° ≤ T ≤ 40°C, where θw, P, and T are wet-bulb potential temperature, pressure, and air temperature.

APA, Harvard, Vancouver, ISO, and other styles

27

De Bruyne, V., F. Leeuwin, and H. Dejonghe. "Orbits in a Stäckel Approximation." International Astronomical Union Colloquium 172 (1999): 395–96. http://dx.doi.org/10.1017/s0252921100072870.

Full text

Abstract:

Because of their analytical simplicity and regularity, Stäckel potentials are attractive tools for modelling galaxies. The third integral I3 is explicitly known in a Stäckel potential, and can be used as an approximation to the effective third integral, in order to construct three-integral models (cf. Dejonghe, et al., 1996, A&A 306, 363).Moreover, Stäckel potentials turn out to yield good global descriptions for either axisymmetric or triaxial systems without central mass concentration (de Zeeuw 1985, MNRAS 216, 273, de Zeeuw & Lynden-Bell 1985, MNRAS 215, 713), and even for some systems with a black hole included (Sridhar & Touma 1997, MNRAS 292, 657).One long-standing concern though, is that Stäckel potentials form only a very small subspace in the family of all potentials. The main orbit families found by numerical integration in general triaxial potentials are present in a Stäckel potential (Schwarzschild 1981, ApJ 232, 236, de Zeeuw 1985, MNRAS 216, 273), but there is obviously no place in an integrable potential for smaller orbital families or stochastic orbits. However, since regular orbits are the rule rather than the exception, a potential which yields a good representation of those orbits is certainly a good basis for building models.

APA, Harvard, Vancouver, ISO, and other styles

28

Gammell, Jonathan D., Timothy D. Barfoot, and Siddhartha S. Srinivasa. "Batch Informed Trees (BIT*): Informed asymptotically optimal anytime search." International Journal of Robotics Research 39, no. 5 (January 27, 2020): 543–67. http://dx.doi.org/10.1177/0278364919890396.

Full text

Abstract:

Path planning in robotics often requires finding high-quality solutions to continuously valued and/or high-dimensional problems. These problems are challenging and most planning algorithms instead solve simplified approximations. Popular approximations include graphs and random samples, as used by informed graph-based searches and anytime sampling-based planners, respectively. Informed graph-based searches, such as A*, traditionally use heuristics to search a priori graphs in order of potential solution quality. This makes their search efficient, but leaves their performance dependent on the chosen approximation. If the resolution of the chosen approximation is too low, then they may not find a (suitable) solution, but if it is too high, then they may take a prohibitively long time to do so. Anytime sampling-based planners, such as RRT*, traditionally use random sampling to approximate the problem domain incrementally. This allows them to increase resolution until a suitable solution is found, but makes their search dependent on the order of approximation. Arbitrary sequences of random samples approximate the problem domain in every direction simultaneously, but may be prohibitively inefficient at containing a solution. This article unifies and extends these two approaches to develop Batch Informed Trees (BIT*), an informed, anytime sampling-based planner. BIT* solves continuous path planning problems efficiently by using sampling and heuristics to alternately approximate and search the problem domain. Its search is ordered by potential solution quality, as in A*, and its approximation improves indefinitely with additional computational time, as in RRT*. It is shown analytically to be almost-surely asymptotically optimal and experimentally to outperform existing sampling-based planners, especially on high-dimensional planning problems.

APA, Harvard, Vancouver, ISO, and other styles

29

Booth, Adam D., Ezgi Emir, and Anja Diez. "Approximations to seismic AVA responses: Validity and potential in glaciological applications." GEOPHYSICS 81, no. 1 (January 1, 2016): WA1—WA11. http://dx.doi.org/10.1190/geo2015-0187.1.

Full text

Abstract:

Amplitude-variation-with-angle (AVA) methods establish the seismic properties of material either side of a reflective interface, and their use is growing in glaciology. The AVA response of an interface is defined by the complex Knott-Zoeppritz (K-Z) equations, numerous approximations to which we typically assume weak interface contrasts and isotropic propagation, inconsistent with the strong contrasts at glacier beds and the vertically transverse isotropic (VTI) fabrics were associated with englacial reflectivity. We considered the validity of a suite of approximate K-Z equations for the exact P-wave reflectivity [Formula: see text] of ice overlying bedrock, sediment and water, and englacial interfaces between isotropic and VTI ice. We found that the approximations of Aki-Richards, Shuey, and Fatti match exact glacier bed reflectivity to within [Formula: see text], smaller than the uncertainty in typical glaciological AVA analyses, but only for maximum incident angle [Formula: see text] limited to 30°. A stricter limit of [Formula: see text] offered comparable accuracy to a hydrocarbon benchmark case of shale overlying gas-charged sand. The VTI-compliant Rüger approximation accurately described englacial reflectivity, to within [Formula: see text], and it can be modified to give a quadratic expression in [Formula: see text] suitable for curve-matching operations. Having shown the circumstances under which AVA approximations were valid for glaciological applications, we have suggested that their interpretative advantages can be exploited in the future AVA interpretations.

APA, Harvard, Vancouver, ISO, and other styles

30

Audzijonis, A., L. Žigas, R. Sereika, and R. Žaltauskas. "Origin of ferroelectric phase transition in SbSClxI1-x mixed crystals." International Journal of Modern Physics B 28, no. 30 (December 4, 2014): 1450209. http://dx.doi.org/10.1142/s0217979214502099.

Full text

Abstract:

The measurements of SbSCl x I 1-x(x = 0.2) temperature dependent capacitance were carried out. The temperature of ferroelectric phase transition TC ≈340 K was measured experimentally. TC of SbSCl x I 1-x was calculated theoretically in anharmonic and harmonic approximations. TC was calculated in anharmonic approximation using temperature dependence of mean potential energy of Sb atoms as a function of the soft B1u symmetry normal coordinate along c(z)-axis. Moreover, TC was calculated in harmonic approximation using temperature dependence of vibrational thermodynamic functions (Helmholc free energy). TC dependence from unit cell parameters a, b and from mixture composition x was carried out.

APA, Harvard, Vancouver, ISO, and other styles

31

Arora, Sandeep, Dharamvir Singh Ahlawat, and Dharambir Singh. "Estimation of Lattice Constants and Band Gaps of Group-III Nitrides using Local and Semi Local Functionals." Oriental Journal of Chemistry 34, no. 4 (July 16, 2018): 2137–43. http://dx.doi.org/10.13005/ojc/3404055.

Full text

Abstract:

We performed the optimization of lattice constants of Group- III nitrides (InN, AlN, GaN) in wurtzite and Zinc blende structures using various semilocal exchange correlation functional in generalized gradient approximations (GGA) namely PBE, WC, PBEsol in addition to local density approximation (LDA) functional. We used these optimized lattice parameters to predict the band gap values using modified Becke Johnson exchange potential with original and improved parameterization as suggested by David Koller for semiconductors having band gap values below 7eV. Among the different functionals considered, PBEsol optimize the lattice parameters with smallest mean error (0.00639 Å) relative to experimental values, while WC approximation with a slightly greater value of mean error (0.00513 Å). It is shown that mBJLDA approximation improves the band gap for the materials studied when compared with LDA and GGA results. It is also shown that LDA optimized parameters with mBJLDA approximation, which leads to mean error of 0.162 eV reproduces the experimental band gap in most efficient way.

APA, Harvard, Vancouver, ISO, and other styles

32

Nadirbekov, M. S., and G. A. Yuldasheva. "Triaxiality in excited states of lanthanide and actinide even–even nuclei." International Journal of Modern Physics E 23, no. 05 (May 2014): 1450034. http://dx.doi.org/10.1142/s0218301314500347.

Full text

Abstract:

The energy levels of excited states of ground state, β- and γ-bands of the lanthanide and actinide even–even nuclei have been studied within the Davydov–Chaban model (for three different types of the potential energy of the β-deformations) and approximations for a small and free triaxiality. It is shown that the approximation with a free triaxiality better describes the spectrum of the excited collective states for considered nuclei.

APA, Harvard, Vancouver, ISO, and other styles

33

Liang, Gui Shu, Xi Xiao Liu, and Shu Wei Zhang. "Model Reduction of Potential Transformer Based on Revised Minimum Information Loss Method." Applied Mechanics and Materials 734 (February 2015): 822–26. http://dx.doi.org/10.4028/www.scientific.net/amm.734.822.

Full text

Abstract:

The circuit model of potential transformer (PT) is indispensable in accurately simulating the electromagnetic characteristic under the lightning overvoltage and very fast transient overvoltage in power systems. This paper utilizes a reduction algorithm for potential transformer based on revised minimum information loss method (RMIL). First, we measured a 10 kV single phase potential transformer using the Agilent 4395A network/spectrum/impedance analyzer. Second, we obtained the rational approximation of two-port circuit parameters by vector fitting (VF). At last, revised minimum information loss method is applied to reduction the state equation of circuit parameters. Comparisons between the reduced and original are given to illustrate the approximating performance of RMIL.

APA, Harvard, Vancouver, ISO, and other styles

34

Fedotov, Aleksey, Alexander Vakhrushev, Olesya Severyukhina, Anatolie Sidorenko, Yuri Savva, Nikolay Klenov, and Igor Soloviev. "Theoretical Basis of Quantum-Mechanical Modeling of Functional Nanostructures." Symmetry 13, no. 5 (May 16, 2021): 883. http://dx.doi.org/10.3390/sym13050883.

Full text

Abstract:

The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and interaction of nuclei and electrons in the framework of the theory of the electron density functional are presented. Common approximations and approaches in the methods of quantum mechanics are presented, including the Born–Oppenheimer approximation, the Hartree–Fock approximation, the Thomas–Fermi theory, the Hohenberg–Kohn theorems, and the Kohn–Sham formalism. Various options for describing the exchange–correlation energy in the theory of the electron density functional are considered, such as the local density approximation, generalized and meta-generalized gradient approximations, and hybridization of the generalized gradient method. The development of methods of quantum mechanics to quantum molecular dynamics or the dynamics of Car–Parrinello is shown. The basic idea of combining classical molecular modeling with calculations of the electronic structure, which is reflected in the potentials of the embedded atom, is described.

APA, Harvard, Vancouver, ISO, and other styles

35

Anikeyev, S. G. "GEODYNAMICS." GEODYNAMICS 2(11)2011, no. 2(11) (September 20, 2011): 18–20. http://dx.doi.org/10.23939/jgd2011.02.018.

Full text

Abstract:

Submitted by fast way to solve the direct problem of 2D/3D gravimetric and magnetic prospecting for complex geological models. Approximating design of models is very dense packing of large numbers of small homogeneous parallelepipeds (108 and over). The method of approximation corresponds to the formulation of linear problems. The developed algorithm can be used to quickly calculate the potential and its derivatives.

APA, Harvard, Vancouver, ISO, and other styles

36

Alston, Steven. "Strong-potential Born-approximation electron-capture cross sections for realistic atomic potentials." Physical Review A 38, no. 6 (September 1, 1988): 3124–27. http://dx.doi.org/10.1103/physreva.38.3124.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

SARKAR, BISWAJIT, LOKENDRA KUMAR SINGH, and DEBRANJAN SARKAR. "A GENETIC ALGORITHM-BASED APPROACH FOR DETECTION OF SIGNIFICANT VERTICES FOR POLYGONAL APPROXIMATION OF DIGITAL CURVES." International Journal of Image and Graphics 04, no. 02 (April 2004): 223–39. http://dx.doi.org/10.1142/s0219467804001385.

Full text

Abstract:

A polygonal approximation captures the essential features of a digital planar curve and yields a compact representation. Those points of the digital curve that carry vital information about the shape of the curve form the vertices of the approximating polygon and are called significant vertices. In this paper, we present a genetic algorithm-based approach to locate a specified number of significant points, such that the approximation error between the original curve and its polygonal version obtained by joining the adjacent significant points is minimized. By using a priori knowledge about the shape of the curve we confine our search to only those points of the curve that have the potential of qualifying as significant points. We also incorporate chromosome differentiation to improve upon the effectiveness of the search in arriving at a near-optimal polygonal approximation. Finally, we show that the proposed method performs remarkably well when evaluated in terms of the metrics available for assessing the goodness of a polygonal approximation algorithm.

APA, Harvard, Vancouver, ISO, and other styles

38

Dukowicz, John K., Stephen F. Price, and William H. Lipscomb. "Consistent approximations and boundary conditions for ice-sheet dynamics from a principle of least action." Journal of Glaciology 56, no. 197 (2010): 480–96. http://dx.doi.org/10.3189/002214310792447851.

Full text

Abstract:

AbstractThe formulation of a physical problem in terms of a variational (or action) principle conveys significant advantages for the analytical formulation and numerical solution of that problem. One such problem is ice-sheet dynamics as described by non-Newtonian Stokes flow, for which the variational principle can be interpreted as stating that a measure of heat dissipation, due to internal deformation and boundary friction, plus the rate of loss of total potential energy is minimized under the constraint of incompressible flow. By carrying out low-aspect-ratio approximations to the Stokes flow problem within this variational principle, we obtain approximate dynamical equations and boundary conditions that are internally consistent and preserve the analytical structure of the full Stokes system. This also allows us to define an action principle for the popular first-order or ‘Blatter–Pattyn’ shallow-ice approximation that is distinct from the action principle for the Stokes problem yet preserves its most important properties and elucidates various details about this approximation. Further approximations within this new action functional yield the standard zero-order shallow-ice and shallow-shelf approximations, with their own action principles and boundary conditions. We emphasize the specification of boundary conditions, which are problematic to derive and implement consistently in approximate models but whose formulation is greatly simplified in a variational setting.

APA, Harvard, Vancouver, ISO, and other styles

39

Kumar, Sandeep, Surender Kumar, and Prabhakar P. Singh. "First-principles Study of Electronic Properties of FeCrxSe Alloys." MRS Advances 1, no. 24 (2016): 1803–9. http://dx.doi.org/10.1557/adv.2016.256.

Full text

Abstract:

ABSTRACTWe performed first-principles study of electronic properties of FeCrxSe (x=0.0, 0.01, 0.02, 0.04) alloys using the Green’s function-based Korringa-Kohn-Rostoker Atomic Sphere Approximation method within the coherent potential approximation (KKR-ASA-CPA). The KKR-ASA-CPA method is implemented with density function theory (DFT). We find that the excess of Cr into FeSe significantly affects the electronic structure with respect to the parent FeSe. The results have been analyzed in terms of changes in the density of states (DOS), partial DOS, band structures, Fermi surface, bare Sommerfeld constant and the superconducting transition temperature of FeCr0.01Se, FeCr0.02Se and FeCr0.04Se alloys respectively. Our calculations show that calculated Tc for these alloys are close to experimental values, given the nature of approximations used in our calculations.

APA, Harvard, Vancouver, ISO, and other styles

40

Masuda-Jindo, Kinichi, Vu Van Hung, and P. E. A. Turchi. "First Principles Calculations of Thermodynamic Quantities and Phase Diagrams of High Temperature BCC Ta-W and Mo-Ta Alloys." Advanced Materials Research 26-28 (October 2007): 205–8. http://dx.doi.org/10.4028/www.scientific.net/amr.26-28.205.

Full text

Abstract:

The thermodynamic properties of high temperature metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The configurational entropy term is taken into account by using the tetrahedron cluster approximation of the cluster variation method (CVM). The energetics of the binary (Ta-W and Mo-Ta) alloys are treated within the framework of the first-principles TB-LMTO (tight-binding linear muffin tin orbital) method coupled to CPA (coherent potential approximation) and GPM (generalized perturbation method). The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys.

APA, Harvard, Vancouver, ISO, and other styles

41

Barrett, James J. C., Howard R. Mayne, Mark Keil, and Leslie J. Rawluk. "Semiclassical study of sudden approximations for rotationally inelastic scattering of Ar + HF." Canadian Journal of Chemistry 72, no. 3 (March 1, 1994): 985–94. http://dx.doi.org/10.1139/v94-127.

Full text

Abstract:

"Exact" quantum close coupled (CC) and infinite-order sudden approximation (IOSA) calculations have been carried out for the Ar + HF system on an accurate potential energy surface. The differential cross sections from the IOSA calculations show marked differences from the CC results. We find that the energy sudden component of the IOSA breaks down in a different manner for small and large impact parameters, significantly shifting and distorting the state-to-state differential cross sections. We also find that the centrifugal sudden approximation alone reproduces all features of the full semiclassical calculations quite faithfully. Through the use of several rotational sudden approximations, including a semiclassical version of the IOSA, we identify how the differences between the CC and IOSA results arise.

APA, Harvard, Vancouver, ISO, and other styles

42

Malyshev, P. V., and A. L. Rebenko. "Approximation by Finite Potentials." Ukrainian Mathematical Journal 65, no. 10 (March 2014): 1490–97. http://dx.doi.org/10.1007/s11253-014-0874-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Benam, Majid, Mauro Ballicchia, Josef Weinbub, Siegfried Selberherr, and Mihail Nedjalkov. "A computational approach for investigating Coulomb interaction using Wigner–Poisson coupling." Journal of Computational Electronics 20, no. 2 (January 21, 2021): 775–84. http://dx.doi.org/10.1007/s10825-020-01643-x.

Full text

Abstract:

AbstractEntangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron–electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron–electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

APA, Harvard, Vancouver, ISO, and other styles

44

Moll, Maximilian, and Leonhard Kunczik. "Comparing quantum hybrid reinforcement learning to classical methods." Human-Intelligent Systems Integration 3, no. 1 (March 2021): 15–23. http://dx.doi.org/10.1007/s42454-021-00025-3.

Full text

Abstract:

AbstractIn recent history, reinforcement learning (RL) proved its capability by solving complex decision problems by mastering several games. Increased computational power and the advances in approximation with neural networks (NN) paved the path to RL’s successful applications. Even though RL can tackle more complex problems nowadays, it still relies on computational power and runtime. Quantum computing promises to solve these issues by its capability to encode information and the potential quadratic speedup in runtime. We compare tabular Q-learning and Q-learning using either a quantum or a classical approximation architecture on the frozen lake problem. Furthermore, the three algorithms are analyzed in terms of iterations until convergence to the optimal behavior, memory usage, and runtime. Within the paper, NNs are utilized for approximation in the classical domain, while in the quantum domain variational quantum circuits, as a quantum hybrid approximation method, have been used. Our simulations show that a quantum approximator is beneficial in terms of memory usage and provides a better sample complexity than NNs; however, it still lacks the computational speed to be competitive.

APA, Harvard, Vancouver, ISO, and other styles

45

EXTREMERA, A. "MACROSCOPIC QUANTUM TUNNELING IN A SUPERCONDUCTING RING CONTAINING A WEAK SUPERCONDUCTING JUNCTION." Modern Physics Letters B 06, no. 24 (October 20, 1992): 1501–11. http://dx.doi.org/10.1142/s0217984992001204.

Full text

Abstract:

Macroscopic quantum effects in SQUIDs are discussed. An equation describing the behavior of the superconducting ring in the harmonic approximation is reduced to the standard form of Mathieu’s equation. For well-defined flux states, good agreement with exact theoretical calculations and experimental results is found near the minimum energy regions. We establish the effective dissipation dependence on tunneling rate via the “instanton” or “bounce” action. WKB-type approximations enable us to obtain the quantum decay rate for a metastable state in the anharmonic (quartic) potential.

APA, Harvard, Vancouver, ISO, and other styles

46

Findlay, Scott D., Mark P. Oxley, and Leslie J. Allen. "Modeling Atomic-Resolution Scanning Transmission Electron Microscopy Images." Microscopy and Microanalysis 14, no. 1 (December 21, 2007): 48–59. http://dx.doi.org/10.1017/s1431927608080112.

Full text

Abstract:

A real-space description of inelastic scattering in scanning transmission electron microscopy is derived with particular attention given to the implementation of the projected potential approximation. A hierarchy of approximations to expressions for inelastic images is presented. Emphasis is placed on the conditions that must hold in each case. The expressions that justify the most direct, visual interpretation of experimental data are also the most approximate. Therefore, caution must be exercised in selecting experimental parameters that validate the approximations needed for the analysis technique used. To make the most direct, visual interpretation of electron-energy-loss spectroscopic images from core-shell excitations requires detector improvements commensurate with those that aberration correction provides for the probe-forming lens. Such conditions can be relaxed when detailed simulations are performed as part of the analysis of experimental data.

APA, Harvard, Vancouver, ISO, and other styles

47

Terletska, Hanna, Yi Zhang, Ka-Ming Tam, Tom Berlijn, Liviu Chioncel, N. Vidhyadhiraja, and Mark Jarrell. "Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems." Applied Sciences 8, no. 12 (November 26, 2018): 2401. http://dx.doi.org/10.3390/app8122401.

Full text

Abstract:

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.

APA, Harvard, Vancouver, ISO, and other styles

48

Zatula, N. I., and D. V. Zatula. "Approximation of density of potentials for the flat viscoelastic bodies with inclusions, bounded by a piecewise smooth contours." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2021): 39–42. http://dx.doi.org/10.17721/1812-5409.2021/1.4.

Full text

Abstract:

An approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potentials along the contours of the inclusions. The approximation of the unknown densities of potentials was performed taking into account the singularity of the stressed state of a flat viscoelastic body near the angular point of the dividing line of the regions.

APA, Harvard, Vancouver, ISO, and other styles

49

Tort, Marine, and Thomas Dubos. "Usual Approximations to the Equations of Atmospheric Motion: A Variational Perspective." Journal of the Atmospheric Sciences 71, no. 7 (June 20, 2014): 2452–66. http://dx.doi.org/10.1175/jas-d-13-0339.1.

Full text

Abstract:

Abstract The usual geophysical approximations are reframed within a variational framework. Starting from the Lagrangian of the fully compressible Euler equations expressed in a general curvilinear coordinates system, Hamilton’s principle of least action yields Euler–Lagrange equations of motion. Instead of directly making approximations in these equations, the approach followed is that of Hamilton’s principle asymptotics; that is, all approximations are performed in the Lagrangian. Using a coordinate system where the geopotential is the third coordinate, diverse approximations are considered. The assumptions and approximations covered are 1) particular shapes of the geopotential; 2) shallowness of the atmosphere, which allows for the approximation of the relative and planetary kinetic energy; 3) small vertical velocities, implying quasi-hydrostatic systems; and 4) pseudoincompressibility, enforced by introducing a Lagangian multiplier. This variational approach greatly facilitates the derivation of the equations and systematically ensures their dynamical consistency. Indeed, the symmetry properties of the approximated Lagrangian imply the conservation of energy, potential vorticity, and momentum. Justification of the equations then relies, as usual, on a proper order-of-magnitude analysis. As an illustrative example, the asymptotic consistency of recently introduced shallow-atmosphere equations with a complete Coriolis force is discussed, suggesting additional corrections to the pressure gradient and gravity.

APA, Harvard, Vancouver, ISO, and other styles

50

Dr.R.Sheelarani, Dr R. Sheelarani, and Dr K. T. Arulmozhi Dr. K.T. Arulmozhi. "On the Use of Function Approximation Potential of Artificial Neural Networks for Predicting Elastic Moduli of Binary Oxide Glass Systems." Global Journal For Research Analysis 3, no. 2 (June 15, 2012): 186–89. http://dx.doi.org/10.15373/22778160/february2014/60.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Approximation du potentiel'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles