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On the Minimum Volume of a Perturbed Unit Cube
[chapter]

2002
*
Lecture Notes in Computer Science
*

We give exact bounds to

doi:10.1007/3-540-36136-7_7
fatcat:pfmb7izjvzhvfnkoqhtj2ja2eu
*the**minimum**volume**of**a*parallelepiped whose spanning vectors are*perturbations**of**the*n*unit*vectors by vectors*of*length at most . ... This extends Micciancio's recent sharp bounds to all possible values*of*. We also completely determine all possible*perturbations*with length at most that achieve this*minimum**volume*. ... Suppose Q is*the**unit**cube*, spanned by*the*n*unit*vectors e 1 = (1, 0, . . . , 0), e 2 = (0, 1, . . . , 0), . . . , e n = (0, 0, . . . , 1), Q = { n i=1*a*i e i | 0 ≤*a*i ≤ 1, 1 ≤ i ≤ n}. (1) Suppose now ...##
###
Instability of the wet cube cone soap film

2005
*
Colloids and Surfaces A: Physicochemical and Engineering Aspects
*

*A*"dry" conical soap film

*on*

*a*cubical frame is not stable. ... This paper presents numerical simulation evidence that

*the*

*the*wet cone is unstable for low enough liquid fraction, with

*the*critical liquid fraction being about 0.000278. ... Given

*the*restricted nature

*of*

*the*

*perturbations*considered, these values only give

*a*lower bound

*on*

*the*true critical

*volume*. ...

##
###
Stearic acid solubility and cubic phase volume

2006
*
Chemistry and Physics of Lipids
*

Below 4% SA/

doi:10.1016/j.chemphyslip.2006.02.016
pmid:16616908
fatcat:uiyu3brdezcxfnijkm5rhzmve4
*volume*(e.g. in acetonitrile),*the*head and foot*of*each SA molecules*on*average is more than*one*solvent molecule away from*the*head and foot*of**a*neighboring SA molecule. ... At 50% SA/cubic*volume*, -CH 2groups*on*SA molecules are separated from neighboring -CH 2 -groups*on*SA molecules by*a*monolayer*of*solvent molecules. ...*The*net dipole moment for*the**cube*is essentially*the*same as for only*one*molecule*of*SA.*On*average for every 13 head groups*of*SA*on*1 surface*of**the**cube*, 12 will be*on**the*opposite*cube*. ...##
###
Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

2021
*
Soft Matter
*

We investigate

doi:10.1039/d1sm00793a
pmid:34251006
fatcat:6y4h3dyw7fcj5jkmn2trk67uba
*the*interaction that occurs between*a*light solid*cube*falling under gravity and*a*horizontal soap film that is pinned to*a*circular ring. We observe in both... ... CR acknowledges support by*the*French government, through*the*National Research Agency (ANR-20-CE30-0019) and through*the*UCA JEDI Investments in*the*Future project*of**the*National Research Agency (ANR ... Acknowledgements We thank Simon Cox for stimulating discussions and Ken Brakke for developing and maintaining*the*Surface Evolver. TD acknowledges Supercomputing Wales facilities. ...##
###
Worst-case bounds for subadditive geometric graphs

1993
*
Proceedings of the ninth annual symposium on Computational geometry - SCG '93
*

We consider graphs such as

doi:10.1145/160985.161018
dblp:conf/compgeom/BernE93
fatcat:4rfc4pvoonbjhbxhcccbrtb3vi
*the**minimum*spanning tree,*minimum*Steiner tree,*minimum*matching, and traveling salesman tour for n points in*the*d-dimensional*unit**cube*. ... This is*a*consequence*of**a*general "gap theorem": for any subadditive geometric graph, either*the*worst-case sum*of*edge lengths is O(n (d−1)/d ) and*the*sum*of*dth powers is O(log n), or*the*sum*of*edge ... For each*of**the*graphs,*a*regular grid*of*points in*the**unit**cube*shows that L(G(X)) is Ω(n (d−1)/d ). ...##
###
On the ratio of the string tension and the glueball mass squared in the continuum

1986
*
Nuclear Physics B
*

We present

doi:10.1016/0550-3213(86)90497-9
fatcat:mswhodgwwne67g3ley4d6l2x6y
*the*weak coupling non-*perturbative*expression for*the*energy*of*'t Hooft type electric flux. ... Combining this with Liischer's*perturbative*scheme for*the*glueball mass M(0+), we propose*a*method to estimate*the*ratio o'/M(0+) 2, with o-*the*string tension. ... SU(2) Yang-Mills*on**a*torus*The*space we work*on*is*the*3-dimensional torus, specified by*a**cube*L x L x L. ...##
###
Calculation of energy relaxation rates of fast particles by phonons in crystals

2015
*
Physical Review B
*

We present ab initio calculations

doi:10.1103/physrevb.91.104305
fatcat:j6wyqtl5prgbdozzw5kz4zgubu
*of**the*temperature-dependent exchange*of*energy between*a*classical charged point-particle and*the*phonons*of**a*crystalline material. ... We discuss*the*influence*of**the*form assumed for quasiparticle dispersion*on*theoretical estimates*of*electron cooling rates. ...*The*subscript s refers to*the**unit*cell and κ refers to*the*sublattice which hosts nuclei*of*charge Z κ .*The*crystal has N repeated*unit*cells which occupy*a**volume*V = N Ω. ...##
###
The optimal centroidal Voronoi tessellations and the gersho's conjecture in the three-dimensional space

2005
*
Computers and Mathematics with Applications
*

We provide abundant evidence to substantiate

doi:10.1016/j.camwa.2004.12.008
fatcat:ouo7ggrfe5fk5fqbviid6ed5ry
*the*claim*of**the*conjecture:*the*body-centered-cubic lattice (or Par6) based centroidal Voronoi tessellation has*the*lowest cost (or energy) per*unit**volume*... In this paper, we conduct extensive numerical simulations to investigate*the*asymptotic structures*of*optimal centroidal Voronoi tessellations for*a*given domain. ... From*the*statistics*of**the*energy per*unit**volume**of**the*final CVTs, it can be seen that there is*a*tendency to approach*the*optimal BCC structure. ...##
###
Description of multi-particle systems using Voronoi polyhedra

2001
*
Powder Technology
*

*The*Ž . Ž . methodology employed herein initiates with

*a*fixed number

*of*particles ranging from 64 to 256

*on*various lattice sites fcc, bcc and sc . ...

*The*position

*of*each particle is then

*perturbed*using three different methods, with

*the*magnitude being controlled by

*the*variable p. ... Acknowledgements

*The*authors appreciate Prof. C.Y. Mou

*of*

*the*Department

*of*Chemistry, National Taiwan University, for providing

*the*VP program. ...

##
###
Shapes and Textures for Rendering Coral
[chapter]

1991
*
Scientific Visualization of Physical Phenomena
*

*The*resulting contour surfaces are rendered by ray tracing, using

*a*generalized

*volume*textare to produce shading and "bump mapped" normal

*perturbations*. ... Abstract

*A*growth algorithm has been developed to build coral shapes out

*of*

*a*tree

*of*spheres.

*A*

*volume*density defined by

*the*spheres is contoured to give

*a*"soft object". ... Department

*of*Energy under contract number W-7405-Eng-48to

*the*Lawrence Livermore NationalLaboratory.We are alsoindebtedto

*the*Universityof Otago WilliamEvans Fund forfinancial supportand to Television ...

##
###
Simulating the interaction between a descending super-quadric solid object and a soap film

2018
*
Proceedings of the Royal Society A
*

We vary

doi:10.1098/rspa.2018.0533
fatcat:tgq7wcp2lbglfpt3tvxymknj7y
*the*shape*of**the*falling object from*a*sphere to*a**cube*by changing*a*single shape parameter as well as varying*the*initial orientation and position*of**the*object. ... We show that*a*cubic particle in*a*particular orientation experiences*the*largest drag force, and that this orientation is also*the*most likely outcome*of*dropping*a**cube*from an arbitrary orientation ... Brakke for providing and supporting*the*Surface Evolver. ...##
###
Page 4071 of Mathematical Reviews Vol. , Issue 91G
[page]

1991
*
Mathematical Reviews
*

In this paper,

*the*authors consider graphs G = (V,,E), whose vertices {x;,---,Xn} form*a*set*of*n points in*the**unit*d-*cube*, i.e. V_ € 0, 1]? ...*a*circuit and*a*pair*of*dual variational principles,*one**of*which we interpret as*a*principle*of**the**minimum**of**the*La- grange potential energy for statics, and*the*other, as*a*principle 90C Mathematical ...##
###
Interface stability in a slowly rotating low-gravity tank

1987
*
Journal of Spacecraft and Rockets
*

*A*summary

*of*

*the*results is shown in Fig. 2, which gives L*,

*the*length

*of*

*the*bubble normalized by

*the*

*cube*root

*of*

*the*bubble

*volume*, as

*a*function

*of*0*,

*the*

*cube*root

*of*pQ? V/(8T)( =[V/R3yJe). ... f, + Uf,/

*A*°), +fy4/(R?

*A*) —f/(R7A)} (16) where

*A*? = 1 + R’? = 1/g?

*on*

*the*free surface. Multiply

*the*momentum equation by

*the*complex conjugate

*of*u and integrate over

*the*liquid

*volume*. ...

##
###
A dissipative particle dynamics method for modeling the geometrical packing of filler particles in polymer composites

2000
*
Journal of Chemical Physics
*

In

doi:10.1063/1.1322636
fatcat:qzwj3n6vuram3j4u4nflyu2cy4
*one*case, entropically driven demixing was observed in*a**cube*-sphere mixture. ...*The*technique is based*on**the*calculation*of**the*dissipative dynamics*of*an ensemble*of*fused soft spheres at constant temperature and pressure. ... They also wish to acknowledge*the*University*of*Cambridge High Performance Computing Facility for*the*use*of*their SGI Origin 2000 computer and associated staff support during*the*course*of*this project ...##
###
Lattice Delone simplices with super-exponential volume

2007
*
European journal of combinatorics (Print)
*

In this short note we give

doi:10.1016/j.ejc.2005.12.003
fatcat:pxaez5qnxrb45pkho7mvatsa6q
*a*construction*of*an infinite series*of*Delone simplices whose relative*volume*grows super-exponentially with their dimension. ... This dramatically improves*the*previous best lower bound, which was linear. ...*The*first author was partially supported by*the*Spanish Ministry*of*Science and Education under grant MTM2005-08618-C02-02. ...
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