The electronic temperature and the effective chemical potential parameters of an atom in a molecule. A Fermi-Dirac semi-local variational approach.

2021 ◽  
Author(s):  
Marco Franco-Perez
Keyword(s):  
Molecular Species ◽  
Variational Approach ◽  
Chemical Potential ◽  
Numerical Procedure ◽  
Electronic Temperature ◽  
Potential Parameters

We developed a numerical procedure to compute the electronic temperature and the effective (local) chemical potential undergone by electrons belonging to a particular molecular species. Our strategy relies on considering...

scholarly journals A Variational Approach and Finite Element Implementation for Swelling of Polymeric Hydrogels Under Geometric Constraints

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Min Kyoo Kang ◽  
Rui Huang
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Variational Approach ◽  
Chemical Potential ◽  
Polymer Network ◽  
Material Model ◽  
Geometric Constraints ◽  
Free Energy Function ◽  
Finite Element Implementation

A hydrogel consists of a cross-linked polymer network and solvent molecules. Depending on its chemical and mechanical environment, the polymer network may undergo enormous volume change. The present work develops a general formulation based on a variational approach, which leads to a set of governing equations coupling mechanical and chemical equilibrium conditions along with proper boundary conditions. A specific material model is employed in a finite element implementation, for which the nonlinear constitutive behavior is derived from a free energy function, with explicit formula for the true stress and tangent modulus at the current state of deformation and chemical potential. Such implementation enables numerical simulations of hydrogels swelling under various constraints. Several examples are presented, with both homogeneous and inhomogeneous swelling deformation. In particular, the effect of geometric constraint is emphasized for the inhomogeneous swelling of surface-attached hydrogel lines of rectangular cross sections, which depends on the width-to-height aspect ratio of the line. The present numerical simulations show that, beyond a critical aspect ratio, creaselike surface instability occurs upon swelling.

scholarly journals Direct Estimation of the Chemical Potential of Molten NaCl by Molecular Dynamics Simulation

1998 ◽  
Vol 53 (1-2) ◽  
pp. 13-16
Author(s):  
Ryuzo Takagi ◽  
Masanori Sakurai
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Chemical Potential ◽  
Dynamics Simulation ◽  
Direct Estimation ◽  
Basic Cell ◽  
Potential Parameters ◽  
Positional Data

Abstract Molecular dynamics simulation of molten NaCl was carried out at 1200 K with well defined potential parameters. The chemical potential of the melt was satisfactorily estimated with the method pro-posed by Powles et al., which requires only positional data of the ions at the temperature in question, when the number of ions in the basic cell is large enough.

scholarly journals CHEMICAL POTENTIAL AS A SOURCE OF STABILITY FOR GRAVITATING SKYRMIONS

2007 ◽  
Vol 22 (39) ◽  
pp. 3003-3011 ◽  
Author(s):  
M. LOEWE ◽  
S. MENDIZABAL ◽  
J. C. ROJAS
Keyword(s):  
Variational Approach ◽  
Chemical Potential ◽  
Radial Profile ◽  
Critical Value ◽  
Winding Number ◽  
Single Particles ◽  
Large N ◽  
Divergent Behavior ◽  
The Stability

A discussion of the stability of self-gravitating Skyrmions, with a large winding number N, in a Schwarzschild type of metric, is presented for the case where an isospin chemical potential is introduced. It turns out that the chemical potential stabilizes the behavior of the Skyrmion discussed previously in the literature. This analysis is carried on in the framework of a variational approach using different ansatze for the radial profile of the Skyrmion. We found a divergent behavior for the size of the Skyrmion, associated to a certain critical value μc of the chemical potential. At this point, the mass of the Skyrmion vanishes. μc is essentially independent of gravitating effects. The stability of a large N skyrmion against decays into single particles is also discussed.

Anisotropic Swelling in Fiber-Reinforced Hydrogels: An Incremental Finite Element Method and Its Applications in Design of Bilayer Structures

2016 ◽  
Vol 08 (07) ◽  
pp. 1640003 ◽  
Author(s):  
Yin Liu ◽  
Hongwu Zhang ◽  
Jianhua Wang ◽  
Yonggang Zheng
Keyword(s):  
Finite Element ◽  
Constitutive Equations ◽  
Chemical Potential ◽  
Numerical Procedure ◽  
Nonlinear Finite Element ◽  
Fiber Reinforced ◽  
Energy Contribution ◽  
Pure Bending ◽  
Tangent Moduli ◽  
Finite Element Procedure

In this paper, we present a theoretical and finite element framework for the inhomogeneous swelling of fiber-reinforced anisotropic hydrogels and investigate the effects of their orientations and moduli on the swelling behaviors of hydrogel bilayers. The effects of fibers on swelling are incorporated into the constitutive equations by introducing the corresponding energy contribution, expressed as the invariants related to the deformation of fibers, into the Flory–Rehner model. Unified constitutive equations and corresponding tangent moduli for anisotropic hydrogels reinforced with two families of fibers are deduced. A nonlinear finite element procedure is developed to simulate the inhomogeneous steady anisotropic swelling, where the chemical potential is prescribed in an incremental way. The accuracy and effectiveness of the numerical procedure are demonstrated by the anisotropic swelling of hydrogel blocks with one or two families of fibers. Based on the numerical procedure, many kinds of swelling configurations for hydrogel bilayers with different fiber orientations and modulus coefficients can be obtained, ranging from pure bending, twisting or saddle-like to combinations of them, which provide systematic guidance for the design of anisotropic-hydrogel based bilayers.

Mathematical model for iron corrosion that eliminates chemical potential parameters

2020 ◽  
Vol 28 (2) ◽  
pp. 603-612 ◽  
Author(s):  
Hadi Seddiqi ◽  
Ali Sadatshojaie ◽  
Behzad Vaferi ◽  
Ehsan Yahyazadeh ◽  
Afshin Salehi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Chemical Potential ◽  
Iron Corrosion ◽  
Potential Parameters

Diagnostics of Gold Laser Plasmas

1988 ◽  
Vol 102 ◽  
pp. 357-360
Author(s):  
J.C. Gauthier ◽  
J.P. Geindre ◽  
P. Monier ◽  
C. Chenais-Popovics ◽  
N. Tragin ◽  
...  
Keyword(s):  
Experimental Results ◽  
Pure Gold ◽  
Electronic Temperature ◽  
X Ray ◽  
Laser Plasmas ◽  
Collisional Radiative Model ◽  
Radiative Model

AbstractIn order to achieve a nickel-like X ray laser scheme we need a tool to determine the parameters which characterise the high-Z plasma. The aim of this work is to study gold laser plasmas and to compare experimental results to a collisional-radiative model which describes nickel-like ions. The electronic temperature and density are measured by the emission of an aluminium tracer. They are compared to the predictions of the nickel-like model for pure gold. The results show that the density and temperature can be estimated in a pure gold plasma.

Chemical potential and dimensions of chain molecules in athermal environments

1996 ◽  
Vol 89 (6) ◽  
pp. 1733-1754 ◽  
Author(s):  
FERNANDO ESCOBEDO ◽  
JUAN DE PABLO
Keyword(s):  
Chemical Potential ◽  
Chain Molecules
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