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

Jin-Yi Cai
2002 Lecture Notes in Computer Science  
We give exact bounds to 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  ... 
doi:10.1007/3-540-36136-7_7 fatcat:pfmb7izjvzhvfnkoqhtj2ja2eu

Instability of the wet cube cone soap film

Kenneth Brakke
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.  ... 
doi:10.1016/j.colsurfa.2004.10.127 fatcat:qilziwgij5bobmyakik6szfaaq

Stearic acid solubility and cubic phase volume

Walter F. Schmidt, Justin R. Barone, Barry Francis, James B. Reeves
2006 Chemistry and Physics of Lipids  
Below 4% SA/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.  ... 
doi:10.1016/j.chemphyslip.2006.02.016 pmid:16616908 fatcat:uiyu3brdezcxfnijkm5rhzmve4

Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

Ioan Tudur Davies, Christophe Raufaste
2021 Soft Matter  
We investigate 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.  ... 
doi:10.1039/d1sm00793a pmid:34251006 fatcat:6y4h3dyw7fcj5jkmn2trk67uba

Worst-case bounds for subadditive geometric graphs

Marshall Bern, David Eppstein
1993 Proceedings of the ninth annual symposium on Computational geometry - SCG '93  
We consider graphs such as 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 ).  ... 
doi:10.1145/160985.161018 dblp:conf/compgeom/BernE93 fatcat:4rfc4pvoonbjhbxhcccbrtb3vi

On the ratio of the string tension and the glueball mass squared in the continuum

Pierre van Baal
1986 Nuclear Physics B  
We present 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.  ... 
doi:10.1016/0550-3213(86)90497-9 fatcat:mswhodgwwne67g3ley4d6l2x6y

Calculation of energy relaxation rates of fast particles by phonons in crystals

M. P. Prange, L. W. Campbell, D. Wu, F. Gao, S. Kerisit
2015 Physical Review B  
We present ab initio calculations 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.  ... 
doi:10.1103/physrevb.91.104305 fatcat:j6wyqtl5prgbdozzw5kz4zgubu

The optimal centroidal Voronoi tessellations and the gersho's conjecture in the three-dimensional space

Qiang Du, Desheng Wang
2005 Computers and Mathematics with Applications  
We provide abundant evidence to substantiate 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.  ... 
doi:10.1016/j.camwa.2004.12.008 fatcat:ouo7ggrfe5fk5fqbviid6ed5ry

Description of multi-particle systems using Voronoi polyhedra

Y.C Liao, D.J Lee, Bing-Hung Chen
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.  ... 
doi:10.1016/s0032-5910(00)00408-3 fatcat:ypcyacnjeff7xbgdlt43svlbei

Shapes and Textures for Rendering Coral [chapter]

Nelson L. Max, Geoff Wyvill
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  ... 
doi:10.1007/978-4-431-68159-5_19 fatcat:cer5jarhanafzelpadz2mjkvri

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

I. T. Davies
2018 Proceedings of the Royal Society A  
We vary 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.  ... 
doi:10.1098/rspa.2018.0533 fatcat:tgq7wcp2lbglfpt3tvxymknj7y

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

ROGER F. GANS, FRED W. LESLIE
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.  ... 
doi:10.2514/3.25904 fatcat:n77s3qcpzzf3vjvsddlajtabye

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

J. A. Elliott, A. H. Windle
2000 Journal of Chemical Physics  
In 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  ... 
doi:10.1063/1.1322636 fatcat:qzwj3n6vuram3j4u4nflyu2cy4

Lattice Delone simplices with super-exponential volume

Francisco Santos, Achill Schürmann, Frank Vallentin
2007 European journal of combinatorics (Print)  
In this short note we give 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.  ... 
doi:10.1016/j.ejc.2005.12.003 fatcat:pxaez5qnxrb45pkho7mvatsa6q
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