Some Criteria for $${\varvec{\mathcal {H}}}$$-Tensors

Wang, Guangbin; Tan, Fuping

doi:10.1007/s42967-019-00059-0

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…Meanwhile, compared with the extensive study of various exact solutions for nonlinear evolution equation, such as soliton solutions and so on, for both discrete and continuous cases, [24][25][26][27][28] the study of interaction solutions has aroused great interest of researchers. [29][30][31][32][33][34] When lump solutions of Eq. (3) is generated through symbolic computations, there is an interesting question that is what kind of interaction solutions can be formulated by combining other kinds of functions?…”

Section: Discussionmentioning

confidence: 99%

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Wang

et al. 2018

Mod. Phys. Lett. B

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Through symbolic computation with Maple, two classes of lump solutions, rationally localized in all directions in space, are presented for a new extended (2[Formula: see text]+[Formula: see text]1)-dimensional Boussinesq equation. Analyticity of the solutions is naturally achieved, and particularly, taking special choices of the involved parameters will guarantee the positiveness of the constant term in the quadratic function f. Moreover, it deserves a note that one parameter in f plays an important role in order to maintain the positiveness of the quadratic function f. As illustrative examples, two particular lump solutions with specific values of the involved parameters are worked out and their three-dimensional plots, contour plots, x-curves and y-curves are made.

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Section: Discussionmentioning

confidence: 99%

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Wang

et al. 2018

Mod. Phys. Lett. B

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“…Equation () is solved using the split‐step Crank–Nicolson method [30, 31, 34], which in turn is based on the finite difference (FD) method. The basic idea of the FD method is to transform the problem of solving a partial differential equation, linear or non‐linear, into a problem of solving a systems of algebraic equations [29], using the discretization of spatial and temporal domains of the wave function and the substitution of derivatives present in the differential equation by approximations involving only numerical values of the wave function [35].…”

Section: Methodsmentioning

confidence: 99%

Dynamics and stability of matter‐wave solitons in cigar‐shaped Bose–Einstein condensates dragged by Pöschl–Teller potential

Pereira

Marangoni

Nascimento

2021

Int J of Quantum Chemistry

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In this paper, we theoretically investigate the dynamics and stability of matter‐wave solitons (MWS) in a cigar‐shaped Bose–Einstein condensate (BEC) consisting of atoms with attractive interatomic interactions trapped by Pöschl–Teller (PT) potential. In this scenario, we propose the idea of the BEC being dragged by PT potential at a constant speed. The BEC was modeled by the quasi‐one‐dimensional Gross–Piteaevskii Equation (1D‐GPE). In addition, an analytical (time‐dependent variational method) and numerical (split‐step Crank–Nicolson method) approach has been proposed to investigate the dynamic properties of solitons during the temporal evolution of this system. Both analytical and numerical results demonstrated that MWSs dragged by PT potential can be stable. From a general point of view, the results obtained in this paper can motivate both theoretical and experimental investigations on the dynamics and stability of solitons in dilute and ultracold unitary Bose gases trapped by PT potential, nonlinear optical properties in PT quantum wells, and propagation of solitons in nonlinear media.

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“…Such timescales are incapable of capturing the essential structural relaxations (such as dynamics of nano-cluster formation/ breakage) and for the prediction of robust rheological properties of these systems at realistic temperatures. In recent studies, coarse-grained (CG) models such as dissipative particle dynamics (DPD) [17,18] and united atom model, [12,19] have been explored for different classes of these complex molecules. However, these models are quite simplistic in their description of the molecules and use limited basis set of potential parameters to distinguish between different aromatic or aliphatic moieties in constituent molecules.…”

Section: Doi: 101002/mats201800040mentioning

confidence: 99%

“…where k is the number of atoms belonging to ellipsoid i and l is that in ellipsoid j. From the same atomistic trajectory, the unit vectors r u ij î ,ˆ, and u ĵ can be computed and the components of the total GB force along the three unit vectors can be evaluated using Equation (17 ,ˆ, and f u ĵ . These forces constitute the set of reference or observed force data against which the CG force field has to be parameterized.…”

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confidence: 99%

Toward Transferable Coarse‐Grained Potentials for Poly‐Aromatic Hydrocarbons: A Force Matching Approach

Tripathy

Agarwal

Kumar

2018

Macro Theory & Simulations

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Poly‐aromatic hydrocarbons (PAHs) have been the subject of numerous experimental investigations for their multitude of existence, from particulate soot to the vast cosmos. Given the structural peculiarity of PAHs, where aromatic moieties serve as the basic building blocks, a generalized coarse‐grained (CG) description befits and holds immense potential to investigate large‐scale PAH systems and their derivatives via CG simulation. Toward this, a minimal CG mapping scheme is proposed where a set of PAHs are modeled as planar molecules made up of oblate ellipsoids, which interact via uniaxial Gay–Berne (GB) potential. A force‐based systematic coarse‐graining approach is followed to extract the CG force field parameters. The resulting GB parameters are found to be either comparable or show definite trends as a function of molecular size. CG simulation is shown to retain the qualitative structural features of the underlying atomistic systems with multi‐fold decrease in computational cost. Accelerated equilibration of atomistic systems is shown to be achievable by MC simulations of CG systems followed by back‐mapping, where the atomistic structure is exactly reproduced.

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Some Criteria for $${\varvec{\mathcal {H}}}$$-Tensors

Abstract: The H-tensor is a new developed concept in tensor analysis and it is an extension of the M-tensor. In this paper, we present some criteria for identifying nonsingular H-tensors and give two numerical examples.

Cited by 8 publications

References 12 publications

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Dynamics and stability of matter‐wave solitons in cigar‐shaped Bose–Einstein condensates dragged by Pöschl–Teller potential

Toward Transferable Coarse‐Grained Potentials for Poly‐Aromatic Hydrocarbons: A Force Matching Approach

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