Van der Waals Interactions of Moving Particles with Surfaces of Cylindrical Geometry

General nonrelativistic theory has been developed and the expressions obtained for the tangential (dissipative) and radial (conservative) image forces and van der Waals forces (vdW) acting on charged and neutral particles when they move parallel to the axis of a cylinder with circular cross-section, or in the space between coaxial cylinders. Numerical calculations of vdW forces have been performed for metal (Au) and dielectric (Si) materials of cylinders (filaments) and Cs atoms at velocities ~107m/s. A remarkable result is that in the case of metal cylinders (atomic filaments and chains) the dynamic vdW potential can be repulsive for certain values of the velocity–distance parameter and the characteristic atomic frequency. In the case of a Si material, the dynamic vdW potential increases relative to the static one (by modulus) when the velocity–distance parameter Vω0/R changes from zero to ~1.3 and then tends to zero.

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Van Der Waal’s Elastica

Applied Mechanics ◽

10.1115/imece2005-82991 ◽

2005 ◽

Cited By ~ 1

Author(s):

Eric Mockensturm ◽

Arash Mahdavi

Keyword(s):

Cross Section ◽

Van Der Waals ◽

Beam Theory ◽

Van Der Waals Forces ◽

Energy Difference ◽

Van Der Waals Interactions ◽

Single Atom ◽

Experimental Investigations ◽

Euler’S Elastica ◽

Additional Strain

Experimental investigations of carbon nanotubes have revealed that they can collapse into nanoribbons that have a dumb-bell shape cross-section. Due to the extreme exibility of single-atom thick graphene sheets, if the tube is large enough self-induced Van der Waals forces acting on the at surfaces of the ribbon will be large enough to hold the nanotube in the collapsed (ribbon) configuration. Energetically, the additional strain (bending) energy stored in the collapsed state is offset by the decrease in energy of the Van der Waals interactions. Because Van der Waals forces are short ranged, one nds that tubes of great enough diameter are bistable. Here we investigate the natural of this bistability by investigating how the energy stored in the tube changes as it is compressed by at rigid indenters of various widths. The nanotube is assumed to deform uniformly along its length and the cross-section is modeled using inextensible, non-linear beam theory (Euler’s Elastica). We nd that the in ated (tube) conguration is always stable but that the energy barrier against decreases with increasing tube radius. Additionally, the energy difference between the in ated and collapsed states decreases nearly linear with increasing radius and for tubes with radius greater than 26 A the collapsed state is energetically favored.

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SAF file: It's really three dimensional file

Mustansiria Dental Journal ◽

10.32828/mdj.v14i1.744 ◽

2018 ◽

Vol 14 (1) ◽

pp. 1

Author(s):

Prof. Dr. Jamal Aziz Mehdi

Keyword(s):

Cross Section ◽

Root Canal ◽

Three Dimensional ◽

Circular Cross Section ◽

Circular Motion ◽

Root Canal Treatment ◽

Metal Core ◽

Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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