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Journal articles on the topic 'Gaussian approximation potentials'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Bartók, Albert P., and Gábor Csányi. "Gaussian approximation potentials: A brief tutorial introduction." International Journal of Quantum Chemistry 115, no. 16 (2015): 1051–57. http://dx.doi.org/10.1002/qua.24927.

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2

Klawohn, Sascha, James R. Kermode, and Albert P. Bartók. "Massively parallel fitting of Gaussian approximation potentials." Machine Learning: Science and Technology 4, no. 1 (2023): 015020. http://dx.doi.org/10.1088/2632-2153/aca743.

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Abstract We present a data-parallel software package for fitting Gaussian approximation potentials (GAPs) on multiple nodes using the ScaLAPACK library with MPI and OpenMP. Until now the maximum training set size for GAP models has been limited by the available memory on a single compute node. In our new implementation, descriptor evaluation is carried out in parallel with no communication requirement. The subsequent linear solve required to determine the model coefficients is parallelised with ScaLAPACK. Our approach scales to thousands of cores, lifting the memory limitation and also deliver

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3

Bartók, Albert P., and Gábor Csányi. "Erratum: Gaussian approximation potentials: A brief tutorial introduction." International Journal of Quantum Chemistry 116, no. 13 (2016): 1049. http://dx.doi.org/10.1002/qua.25140.

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4

Hiroshima, Fumio. "A Scaling Limit of a Hamiltonian of Many Nonrelativistic Particles Interacting with a Quantized Radiation Field." Reviews in Mathematical Physics 09, no. 02 (1997): 201–25. http://dx.doi.org/10.1142/s0129055x97000075.

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This paper presents a scaling limit of Hamiltonians which describe interactions of N-nonrelativistic charged particles in a scalar potential and a quantized radiation field in the Coulomb gauge with the dipole approximation. The scaling limit defines effective potentials. In one-nonrelativistic particle case, the effective potentials have been known to be Gaussian transformations of the scalar potential [J. Math. Phys.34 (1993) 4478–4518]. However it is shown that the effective potentials in the case of N-nonrelativistic particles are not necessary to be Gaussian transformations of the scalar

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5

John, S. T., and Gábor Csányi. "Many-Body Coarse-Grained Interactions Using Gaussian Approximation Potentials." Journal of Physical Chemistry B 121, no. 48 (2017): 10934–49. http://dx.doi.org/10.1021/acs.jpcb.7b09636.

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6

FUKUKAWA, K., Y. FUJIWARA, and Y. SUZUKI. "GAUSSIAN NONLOCAL POTENTIALS FOR THE QUARK-MODEL BARYON–BARYON INTERACTIONS." Modern Physics Letters A 24, no. 11n13 (2009): 1035–38. http://dx.doi.org/10.1142/s021773230900053x.

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Gaussian nonlocal potentials for the quark-model baryon–baryon interactions are derived by using the Gauss-Legendre quadrature for the special functions. The reliability of the approximation is examined with respect to the phase shifts and the deuteron binding energy. The potential is accurate enough if one uses seven-point Gauss-Legendre quadrature.

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7

SÉNÉCHAL, DAVID. "CHAOS IN THE HERMITIAN ONE-MATRIX MODEL." International Journal of Modern Physics A 07, no. 07 (1992): 1491–506. http://dx.doi.org/10.1142/s0217751x9200065x.

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The recursion coefficients Ri, which appear in the orthogonal polynomial method of solution for the Hermitian one-matrix model, are determined numerically for values of N up to a thousand. For some cases a chaotic behavior appears in some range, preventing a smooth flow from odd to even multicrititical models. This behavior is studied both for single-well and multiwell potentials. For multiwell potentials, the coefficients Ri generically tend toward more than one function in the N→∞ limit, and this structure is analyzed for small i using the Gaussian approximation.

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8

Demiroğlu, İlker, Yenal Karaaslan, Tuğbey Kocabaş, Murat Keçeli, Álvaro Vázquez-Mayagoitia, and Cem Sevik. "Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials." Journal of Physical Chemistry C 125, no. 26 (2021): 14409–15. http://dx.doi.org/10.1021/acs.jpcc.1c01888.

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9

Exl, Lukas, Norbert J. Mauser, and Yong Zhang. "Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation." Journal of Computational Physics 327 (December 2016): 629–42. http://dx.doi.org/10.1016/j.jcp.2016.09.045.

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10

OLSEN, R. A., та F. RAVNDAL. "EFFECTIVE POTENTIALS FOR ϕ4-THEORY IN 2+1 DIMENSIONS". Modern Physics Letters A 09, № 28 (1994): 2623–35. http://dx.doi.org/10.1142/s021773239400246x.

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Spontaneous symmetry breaking in ϕ4-theory in 2+1 dimensions is investigated using the Gaussian approximation. The theory stays in the symmetric phase at zero temperature as long as the bare coupling constant is below a critical value λc. When λ>λc the symmetric phase is again stable when the temperature is above a transition temperature T(λ). The obtained results are compared with the predictions of the standard one-loop effective potential.

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11

Delgadillo, Ricardo, Jianfeng Lu, and Xu Yang. "Gauge-Invariant Frozen Gaussian Approximation Method for the Schrödinger Equation with Periodic Potentials." SIAM Journal on Scientific Computing 38, no. 4 (2016): A2440—A2463. http://dx.doi.org/10.1137/15m1040384.

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12

Kim, M. H., and Dick K. P. Yue. "Sum-and Difference-Frequency Wave Loads on a Body in Unidirectional Gaussian Seas." Journal of Ship Research 35, no. 02 (1991): 127–40. http://dx.doi.org/10.5957/jsr.1991.35.2.127.

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When nonlinear effects are included in the diffraction of waves by a large body, there are, at second order, interactions at the sums and differences of the component frequencies of the incident waves. In this paper, the complete deterministic and stochastic solutions of second-order (sum-and difference-frequency) wave loads in unidirectional Gaussian waves are considered. The deterministic result, namely the wave force quadratic transfer function (QTF) in bichromatic incident waves, is complete in the context of second-order diffraction theory in that all the relevant components including tho

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13

Koch, Wolfhard, Klaus Neymeyr, Markus Pernpointner, Barbara Schaper, and Klaus Strecker. "Simplified Non-Empirical Unrestricted Hartree-Fock Approximation (SUHF) for the Calculation of Electronic Ground State Properties of Molecules with Closed and Open Valence Shells. II. Diatomic Molecules." Zeitschrift für Naturforschung A 48, no. 7 (1993): 834–40. http://dx.doi.org/10.1515/zna-1993-0715.

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Abstract A comparison of numerical Simplified Unrestricted Hartree-Fock (SUHF) results (electronic ground state configurations, total energies, first ionization potentials, atomic charges, atomic spin densities of diatomic molecules) with those of equivalent standard calculations suggests the applicability of the non-empirical but drastically simplified procedure. SUHF may even approach ab initio quality obtained with simple (STO-3G) contracted Gaussian basis sets.

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14

Fang, Di, and Lei Li. "Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 2 (2020): 431–63. http://dx.doi.org/10.1051/m2an/2019067.

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The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the movement of microparticles with sub-diffusion phenomenon. It has been proved that with fractional Gaussian noise (fGn) mostly considered by biologists, the overdamped Generalized Langevin equation satisfying fluctuation dissipation theorem can be written as a fractional stochastic differential equation (FSDE). In this work, we present both a direct and a fast algorithm respectively for this FSDE model in order to numerically study ergodicity. The strong orders of convergence

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15

Austen, Maggie A., Leif A. Eriksson, and Russell J. Boyd. "A density functional theory study of the free radicals NH2, NF2, NCl2, PH2, PF2, and PCl2." Canadian Journal of Chemistry 72, no. 3 (1994): 695–704. http://dx.doi.org/10.1139/v94-094.

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The linear combination of Gaussian-type orbitals–density functional theory (LCGTO–DFT) approach is used to study geometries and hyperfine structures of a set of neutral radicals. Each of the title molecules is investigated by means of local density approximation calculations, and using the Becke–Perdew and Perdew–Wang–Perdew corrections to the exchange and correlation functionals. The effects of local vs. non-local potentials and of various basis sets are investigated. Total densities and unpaired spin densities are compared. The isotropic couplings are found to be very dependent on the type o

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16

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 (2018): 20170138. http://dx.doi.org/10.1098/rsta.2017.0138.

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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 f

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17

Nguyen, Thuong T., Eszter Székely, Giulio Imbalzano, et al. "Comparison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in representing water interactions through many-body expansions." Journal of Chemical Physics 148, no. 24 (2018): 241725. http://dx.doi.org/10.1063/1.5024577.

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18

Staacke, Carsten G., Tabea Huss, Johannes T. Margraf, Karsten Reuter, and Christoph Scheurer. "Tackling Structural Complexity in Li2S-P2S5 Solid-State Electrolytes Using Machine Learning Potentials." Nanomaterials 12, no. 17 (2022): 2950. http://dx.doi.org/10.3390/nano12172950.

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The lithium thiophosphate (LPS) material class provides promising candidates for solid-state electrolytes (SSEs) in lithium ion batteries due to high lithium ion conductivities, non-critical elements, and low material cost. LPS materials are characterized by complex thiophosphate microchemistry and structural disorder influencing the material performance. To overcome the length and time scale restrictions of ab initio calculations to industrially applicable LPS materials, we develop a near-universal machine-learning interatomic potential for the LPS material class. The trained Gaussian Approxi

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19

Merchant, A. C. "The generation of rotational bands by deep, diffuse potentials." Canadian Journal of Physics 66, no. 4 (1988): 295–301. http://dx.doi.org/10.1139/p88-045.

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Numerical integration of the single-particle Schrödinger equation containing a deep, diffuse, spherically symmetric, attractive, local potential often gives rise to bound-state energy eigenvalues, which lie on almost perfect rotational bands. Each band is characterized by a constant value of (2n + l), where n is the number of interior nodes in the radial wave function and l is the orbital angular-momentum quantum number of a member state. The constants of near-proportionality between the state energies and l(l + 1) for the various bands are considered. An expression for them derived from the B

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20

GAO, XIANLONG, M. POLINI, M. P. TOSI, and B. TANATAR. "EFFECT OF DISORDER ON THE INTERACTING FERMI GASES IN A ONE-DIMENSIONAL OPTICAL LATTICE." International Journal of Modern Physics B 22, no. 25n26 (2008): 4500–4510. http://dx.doi.org/10.1142/s0217979208050255.

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Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The

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21

Timmermann, Jakob, Yonghyuk Lee, Carsten G. Staacke, Johannes T. Margraf, Christoph Scheurer, and Karsten Reuter. "Data-efficient iterative training of Gaussian approximation potentials: Application to surface structure determination of rutile IrO₂ and RuO₂." Journal of Chemical Physics 155, no. 24 (2021): 244107. http://dx.doi.org/10.1063/5.0071249.

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22

Alexandrov, Artem A., Alina U. Badamshina, and Stanislav L. Ogarkov. "Quantum Gases of Dipoles, Quadrupoles and Octupoles in Gross–Pitaevskii Formalism with Form Factor." Condensed Matter 5, no. 4 (2020): 61. http://dx.doi.org/10.3390/condmat5040061.

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Here, classical and quantum field theory of dipolar, axisymmetric quadrupolar and octupolar Bose gases is considered within a general approach. Dipole, axisymmetric quadrupole and octupole interaction potentials in the momentum representation are calculated. These results clearly demonstrate attraction and repulsion areas in corresponding gases. Then the Gross–Pitaevskii (GP) equation, which plays a key role in the present paper, is derived from the corresponding functional. The zoology of the form factors appearing in the GP equation is studied in details. The proper classes for the descripti

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23

Cea, Paolo. "Gaussian effective potential beyond the gaussian approximation." Physics Letters B 236, no. 2 (1990): 191–95. http://dx.doi.org/10.1016/0370-2693(90)90826-r.

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24

Bernardi, Davide, and Benjamin Lindner. "A frequency-resolved mutual information rate and its application to neural systems." Journal of Neurophysiology 113, no. 5 (2015): 1342–57. http://dx.doi.org/10.1152/jn.00354.2014.

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The encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon's information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low- or high-pass filtering of information, i.e., the selective coding of slow or fas

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25

Sokolovsky, A. I. "Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory." Journal of Physics and Electronics 28, no. 2 (2020): 63–74. http://dx.doi.org/10.15421/332022.

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Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions

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26

Burkitt, A. N., and G. M. Clark. "Calculation of Interspike Intervals for Integrate-and-Fire Neurons with Poisson Distribution of Synaptic Inputs." Neural Computation 12, no. 8 (2000): 1789–820. http://dx.doi.org/10.1162/089976600300015141.

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We present a new technique for calculating the interspike intervals of integrate-and-fire neurons. There are two new components to this technique. First, the probability density of the summed potential is calculated by integrating over the distribution of arrival times of the afferent post-synaptic potentials (PSPs), rather than using conventional stochastic differential equation techniques. A general formulation of this technique is given in terms of the probability distribution of the inputs and the time course of the postsynaptic response. The expressions are evaluated in the gaussian appro

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27

COTĂESCU, ION I., PAUL GRĂVILĂ, and MARIUS PAULESCU. "PSEUDO-GAUSSIAN OSCILLATORS." International Journal of Modern Physics C 19, no. 10 (2008): 1607–15. http://dx.doi.org/10.1142/s012918310801314x.

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A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic oscillator when x → 0. These models give rise to approximative equidistant energy levels of bound states and resonances as it is shown using numerical calculations based on an efficient method of generating functionals.

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28

Lu, Wen-Fa, Chul Koo Kim, and Kyun Nahm. "Sine-Gordon effective potential beyond Gaussian approximation." Physics Letters B 546, no. 1-2 (2002): 177–88. http://dx.doi.org/10.1016/s0370-2693(02)02659-x.

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29

YAHYA, G. A. "DEFORMED OPTICAL POTENTIAL ANALYSES FOR P+12C." International Journal of Modern Physics E 13, no. 04 (2004): 851–66. http://dx.doi.org/10.1142/s0218301304002508.

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The high energy single folding optical potential approximation is studied to calculate the differential cross-section for proton elastic scattering of 12 C at 156 MeV and 1440 MeV and 12 C for state 2+ (4.44 MeV) at 1440 MeV. A Gaussian nuclear density distribution was used for the proton and Gaussian and Brink nuclear density distributions for the 12 C target. We used the following three effects to derive twelve different methods for the central optical potential: (i) Love and Franey and the Gaussian amplitudes, with the Brink and one-term Gaussian nuclear density distributions, (ii) Pauli co

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30

Bingham, N., and Tasmin Symons. "Gaussian random fields: with and without covariances." Theory of Probability and Mathematical Statistics 106 (May 16, 2022): 27–40. http://dx.doi.org/10.1090/tpms/1163.

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We begin with isotropic Gaussian random fields, and show how the Bochner–Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Matérn processes on Euclidean space, spheres, manifolds and graphs, using Bessel potentials and stochastic partial differential equations (SPDEs). We then turn from this continuous setting to approximating discrete settings, Gaussian Markov random fields (GMRFs), and the computational advantages they bring in handling large data sets, by exploiting the sparseness properties of the relevant precision (concentration) mat

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31

Zhang, Cunzhi, and Qiang Sun. "Gaussian approximation potential for studying the thermal conductivity of silicene." Journal of Applied Physics 126, no. 10 (2019): 105103. http://dx.doi.org/10.1063/1.5119281.

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32

Fujikake, So, Volker L. Deringer, Tae Hoon Lee, Marcin Krynski, Stephen R. Elliott, and Gábor Csányi. "Gaussian approximation potential modeling of lithium intercalation in carbon nanostructures." Journal of Chemical Physics 148, no. 24 (2018): 241714. http://dx.doi.org/10.1063/1.5016317.

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33

George, Janine, Geoffroy Hautier, Albert P. Bartók, Gábor Csányi, and Volker L. Deringer. "Combining phonon accuracy with high transferability in Gaussian approximation potential models." Journal of Chemical Physics 153, no. 4 (2020): 044104. http://dx.doi.org/10.1063/5.0013826.

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34

Leboeuf, M., A. M. Köster, and D. R. Salahub. "Approximation of the molecular electrostatic potential in a gaussian density functional method." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 96, no. 1 (1997): 23–30. http://dx.doi.org/10.1007/s002140050199.

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35

Harris, John G. "The Wavefield Radiated Into an Elastic Half-Space by a Transducer of Large Aperture." Journal of Applied Mechanics 55, no. 2 (1988): 398–404. http://dx.doi.org/10.1115/1.3173689.

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The wavefield radiated into an elastic half-space by an ultrasonic transducer, as well as the radiation admittance of the transducer coupled to the half-space, are studied. Two models for the transducer are used. In one an axisymmetric, Gaussian distribution of normal traction is imposed upon the surface, while in the other a uniform distribution of normal traction is imposed upon a circular region of the surface, leaving the remainder free of traction. To calculate the wavefield, each wave emitted by the transducer is expressed as a plane wave multiplied by an asymptotic power series in inver

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36

Lahkar, Jugal, Rashidul Hoque, and D. K. Choudhury. "Masses of heavy–light mesons with two-loop static potential in a variational approach." Modern Physics Letters A 34, no. 14 (2019): 1950106. http://dx.doi.org/10.1142/s0217732319501062.

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In this work, we investigate the masses of a few heavy–light mesons with variational method, taking into account the two-loop effects in the static Cornell potential. Specifically, we consider two wave functions, Gaussian and Coulomb. Our analysis suggests that phenomenologically such approach is more successful in the heavy flavored meson sector than the stationary state perturbation theory and other approximation methods.

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37

Boukahil, A., and D. L. Huber. "Coherent potential approximation for the absorption spectra of a two-dimensional Frenkel exciton system with Gaussian diagonal disorder." Modern Physics Letters B 28, no. 32 (2014): 1450251. http://dx.doi.org/10.1142/s0217984914502510.

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We investigate the optical absorption and the density of states of a Frenkel exciton system on a square lattice with nearest-neighbor interactions and a Gaussian distribution of transition frequencies (i.e. Gaussian diagonal disorder). Results are presented for the absorption and the density of states of direct and indirect edge systems for a range of variances. There is reasonable agreement with the corresponding finite array calculations of Schreiber and Toyozawa. The existence of an Urbach tail is also investigated.

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38

Sharma, A., and M. Sheinman. "Analytical approximation for chemical potential in organic materials with Gaussian density of states." Journal of Physics D: Applied Physics 46, no. 12 (2013): 125106. http://dx.doi.org/10.1088/0022-3727/46/12/125106.

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39

Fabčič, Tomaž, Jörg Main, and Günter Wunner. "Fictitious-Time Wave-Packet Dynamics in Atomic Systems." Zeitschrift für Naturforschung A 65, no. 10 (2010): 871–76. http://dx.doi.org/10.1515/zna-2010-1015.

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Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with non-singular smooth potentials. They are rare in atomic systems on account of the singular behaviour of the Coulomb potential.We present a time-dependent variational method that makes the use of GWPs possible in the description of propagation of quantum states also in these systems. We use a regularization of the Coulomb potential and introduce a fictitious-time coordinate in which the evolution of an initial state can be calculated exactly and analytically

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40

Fouokeng, Georges Collince, Martin Tchoffo, Lukong Cornelius Fai, Ngwa Engelbert Afuoti, J. C. Ngana Kuetche, and A. M. Temgoua Nouaze. "The quenching field effect on the motion of an electron in an electromagnetic field potential." Modern Physics Letters B 28, no. 08 (2014): 1450058. http://dx.doi.org/10.1142/s0217984914500584.

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In this paper, the Feynman path integral approach based on the Gaussian wave packet approximation is employed to evaluate the coherence factor and the probability distribution for a single electron subjected to a magnetic field tailored by a variable on/off force. The quenching field effect is observed to create decoherence in the motion of the electron. The coherence factor is observed to decrease while the distribution probability function shows dephasing characteristics for weak and strong field strengths.

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41

Senff, UE, and PC Burton. "A CEPA2 Study of the H2?H2 Isotropic Potential Function." Australian Journal of Physics 42, no. 1 (1989): 47. http://dx.doi.org/10.1071/ph890047.

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A CEPA2 study of the DDl (Koide and Kihara 1974) conformation of two hydrogen molecules has been carried out using a basis set consisting of 102 independent gaussian functions to describe the interacting system. Calculations using a smal\er basis set indicate that this conformation provides a close approximation to the isotropic Vooo potential function. The study was carried out for intermolecular separations ranging from R = 2�0 to 15�0 a.u. keeping the H2 bond lengths fixed at r = 1 �449 a.u. The wel\ depth was determined to be 104� 73/ih at Rm = 6�597 a.u. and the zero point crossing at Ro

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42

BHAGWAT, K. V., S. V. LAWANDE, and D. C. KHANDEKAR. "ON THE DENSITY OF ELECTRONIC STATES OF TWO-DIMENSIONAL POSITIONALLY DISORDERED SYSTEMS WITH WEAK ELECTRON-ION POTENTIAL." International Journal of Modern Physics B 01, no. 05n06 (1987): 1321–28. http://dx.doi.org/10.1142/s0217979287001742.

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The path-integral formulation of Edwards and Gulyaev has been used to investigate the behaviour of electronic density of states in the two-dimensional positionally disordered systems. The average electron propagator is evaluated within the first cumulant approximation. It is shown that in general the two-dimensional system possesses a non-zero density of states in the band-tail region. In particular an expression for the density of states for a Gaussian model of a two-dimensional disordered system is derived. Numerical values of density of states for this model for some typical values of param

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43

Maignan, Aude, and Tony Scott. "A Comprehensive Analysis of Quantum Clustering : Finding All the Potential Minima." International Journal of Data Mining & Knowledge Management Process 11, no. 1 (2021): 33–54. http://dx.doi.org/10.5121/ijdkp.2021.11103.

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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a σ value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This i

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44

Karki, Bhishma, Saddam Husain Dhobi, Jeevan Jyoti Nakarmi, and Kishori Yadav. "Energy Eigenvalue and Thermodynamic Properties of q-deformed Hulthen Potential." BIBECHANA 19, no. 1-2 (2022): 165–69. http://dx.doi.org/10.3126/bibechana.v19i1-2.46416.

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The objective of this work is to calculate the energy eigenvalue for q-deformed Hulthen potential using a Gaussian hypergeometric function with centrifugal approximation factor and related thermodynamical properties. For this, we develop a mathematical model using the Schrodinger wave equation to find the energy eigenvalue. In addition, the thermodynamic parameters were also calculated for q-deformed Hulthen potential using the partition function. The energy eigenvalue for quantum numbers n=1 to n=5 was observed for screening parameters 0.1, 0.5, and 1. In between, 0.1 to 1 and n=1 to n=2 the

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45

Wang, Yaqin, Yi Luo, and Muhammad Shafeeque. "Using a Gaussian Function to Describe the Seasonal Courses of Monthly Precipitation and Potential Evapotranspiration across the Yellow River Basin, China." Journal of Hydrometeorology 20, no. 11 (2019): 2185–201. http://dx.doi.org/10.1175/jhm-d-19-0019.1.

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Abstract Seasonal variations in precipitation (P) and potential evapotranspiration (ET0) are critical for regional hydrometeorological studies and water resource management. The sinusoidal function is widely used to describe the seasonal pattern of P and ET0. However, high errors occur either in the arid places or in places with hyperseasonal precipitation. These limitations are intrinsic properties of the sinusoidal climate descriptor and remain a barrier to provide insight into regional water–energy partitions and hydrologic similarity and predictability. In this study, we used a Gaussian fr

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Landscheid, Ulf, and Werner Kutzelnigg. "On the accuracy of conventional calculations of potential energy surfaces." Collection of Czechoslovak Chemical Communications 53, no. 9 (1988): 1953–60. http://dx.doi.org/10.1135/cccc19881953.

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It is demonstrated for the example of H2+ that with the conventional basis expansion method (in terms of Gaussians) with fixed non-linear parameters the error of a computed potential curve varies strongly with the geometry. If the non-linear parameters are optimized for the equilibrium geometry, much larger errors arise for other geometries. This is very pronounced if only one polarization function of a given l is added to the basis, and qualitatively the same problem arises for any new l. The dependence of the error on the distance may also be oscillatory. For the example of Li2 in the SCF or

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Mocanu, F. C., K. Konstantinou, and S. R. Elliott. "Quench-rate and size-dependent behaviour in glassy Ge2Sb2Te5 models simulated with a machine-learned Gaussian approximation potential." Journal of Physics D: Applied Physics 53, no. 24 (2020): 244002. http://dx.doi.org/10.1088/1361-6463/ab77de.

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Zhang, Linfeng, Han Wang, Maria Carolina Muniz, Athanassios Z. Panagiotopoulos, Roberto Car, and Weinan E. "A deep potential model with long-range electrostatic interactions." Journal of Chemical Physics 156, no. 12 (2022): 124107. http://dx.doi.org/10.1063/5.0083669.

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Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and val

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Delgadillo, Ricardo, and Di Liu. "A Spectral Algorithm for the Time-Dependent Kohn--Sham Equations: Accurately Treating External Potentials Based on Frozen Gaussian Approximations." SIAM Journal on Scientific Computing 42, no. 3 (2020): B656—B674. http://dx.doi.org/10.1137/19m1245104.

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Nakamura, Issei, and V. Dmitrašinović. "Linear model in the Gaussian wave functional approximation II: analyticity of the S-matrix and the effective potential/action." Nuclear Physics A 713, no. 1-2 (2003): 133–47. http://dx.doi.org/10.1016/s0375-9474(02)01293-9.

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