scholarly journals A Mathematical Analysis of Casimir Interactions I: The Scalar Field

2021 ◽  
Author(s):  
Yan-Long Fang ◽  
Alexander Strohmaier
Keyword(s):  
Scalar Field ◽  
Mathematical Analysis ◽  
Casimir Forces ◽  
Casimir Interactions

AbstractStarting from the construction of the free quantum scalar field of mass $$m\ge 0$$ m ≥ 0 , we give mathematically precise and rigorous versions of three different approaches to computing the Casimir forces between compact obstacles. We then prove that they are equivalent.

scholarly journals Stress tensor for a scalar field in a spatially varying background potential: Divergences, “renormalization”, anomalies, and Casimir forces

2016 ◽  
Vol 93 (8) ◽  
Author(s):  
Kimball A. Milton ◽  
Stephen A. Fulling ◽  
Prachi Parashar ◽  
Pushpa Kalauni ◽  
Taylor Murphy
Keyword(s):  
Scalar Field ◽  
Stress Tensor ◽  
Casimir Forces ◽  
Spatially Varying

scholarly journals Critical Casimir interactions around the consolute point of a binary solvent

Soft Matter ◽  
2014 ◽  
Vol 10 (30) ◽  
pp. 5510-5522 ◽  
Author(s):  
T. F. Mohry ◽  
S. Kondrat ◽  
A. Maciołek ◽  
S. Dietrich
Keyword(s):  
Phase Behavior ◽  
Colloidal Suspensions ◽  
Binary Solvent ◽  
Casimir Forces ◽  
Thermodynamic State ◽  
Consolute Point ◽  
Casimir Interactions

Critical Casimir forces between colloids depend sensitively on the thermodynamic state of the solvent which is reflected in the phase behavior of colloidal suspensions.

scholarly journals Casimir force and its effects on pull-in instability modelled using molecular dynamics simulations

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200311
Author(s):  
Avirup Sircar ◽  
Puneet Kumar Patra ◽  
Romesh C. Batra
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Casimir Force ◽  
Casimir Effect ◽  
Md Simulations ◽  
Casimir Forces ◽  
Total Potential ◽  
Continuum Scale ◽  
Casimir Interactions ◽  
Dynamics Simulations

We present a new methodology to incorporate the Casimir forces within the molecular dynamics (MD) framework. At atomistic scales, the potential energy between two particles arising due to the Casimir effect can be represented as U ( r ij ) =  C / r 7 . Incorporating the Casimir effect in MD simulations requires the knowledge of C , a problem hitherto unsolved. We overcome this by equating the total potential energy contributions due to each atomistic pair with the potential energy of continuum scale interacting bodies having similar geometries. After having identified the functional form of C , standard MD simulations are augmented with the potential energy contribution due to pairwise Casimir interactions. The developed framework is used to study effects of the Casimir force on the pull-in instability of rectangular and hollow cylindrical shaped deformable electrodes separated by a small distance from a fixed substrate electrode. Our MD results for pull-instability qualitatively agree with the previously reported analytical results but are quantitatively different. The effect of using longer-ranged Casimir forces in a constant temperature environment on the pull-in behaviour has also been studied.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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