58,234 research outputs found
The strong thirteen spheres problem
The thirteen spheres problem is asking if 13 equal size nonoverlapping
spheres in three dimensions can touch another sphere of the same size. This
problem was the subject of the famous discussion between Isaac Newton and David
Gregory in 1694. The problem was solved by Schutte and van der Waerden only in
1953.
A natural extension of this problem is the strong thirteen spheres problem
(or the Tammes problem for 13 points) which asks to find an arrangement and the
maximum radius of 13 equal size nonoverlapping spheres touching the unit
sphere. In the paper we give a solution of this long-standing open problem in
geometry. Our computer-assisted proof is based on a enumeration of the
so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag
Revised self-consistent continuum solvation in electronic-structure calculations
The solvation model proposed by Fattebert and Gygi [Journal of Computational
Chemistry 23, 662 (2002)] and Scherlis et al. [Journal of Chemical Physics 124,
074103 (2006)] is reformulated, overcoming some of the numerical limitations
encountered and extending its range of applicability. We first recast the
problem in terms of induced polarization charges that act as a direct mapping
of the self-consistent continuum dielectric; this allows to define a functional
form for the dielectric that is well behaved both in the high-density region of
the nuclear charges and in the low-density region where the electronic
wavefunctions decay into the solvent. Second, we outline an iterative procedure
to solve the Poisson equation for the quantum fragment embedded in the solvent
that does not require multi-grid algorithms, is trivially parallel, and can be
applied to any Bravais crystallographic system. Last, we capture some of the
non-electrostatic or cavitation terms via a combined use of the quantum volume
and quantum surface [Physical Review Letters 94, 145501 (2005)] of the solute.
The resulting self-consistent continuum solvation (SCCS) model provides a very
effective and compact fit of computational and experimental data, whereby the
static dielectric constant of the solvent and one parameter allow to fit the
electrostatic energy provided by the PCM model with a mean absolute error of
0.3 kcal/mol on a set of 240 neutral solutes. Two parameters allow to fit
experimental solvation energies on the same set with a mean absolute error of
1.3 kcal/mol. A detailed analysis of these results, broken down along different
classes of chemical compounds, shows that several classes of organic compounds
display very high accuracy, with solvation energies in error of 0.3-0.4
kcal/mol, whereby larger discrepancies are mostly limited to self-dissociating
species and strong hydrogen-bond forming compounds.Comment: The following article has been accepted by The Journal of Chemical
Physics. After it is published, it will be found at
http://link.aip.org/link/?jcp
Monte Carlo simulation of nonlinear Couette flow in a dilute gas
The Direct Simulation Monte Carlo method is applied to solve the Boltzmann
equation in the steady planar Couette flow for Maxwell molecules and hard
spheres. Nonequilibrium boundary conditions based on the solution of the
Bhatnagar-Gross-Krook (BGK) model for the Couette flow are employed to diminish
the influence of finite-size effects. Non-Newtonian properties are
characterized by five independent generalized transport coefficients: a
viscosity function, a thermal conductivity function, two viscometric functions,
and a cross coefficient measuring the heat flux orthogonal to the thermal
gradient. These coefficients depend nonlinearly on the shear rate. The
simulation results are compared with theoretical predictions given by the Grad
method and the BGK and the ellipsoidal statistical (ES) models. It is found
that the kinetic models present a good agreement with the simulation,
especially in the case of the ES model, while the Grad method is only
qualitatively reliable for the momentum transport. In addition, the velocity
distribution function is also measured and compared with the BGK and ES
distributions.Comment: 25 pages (including 15 figures); minor changes; revised version
accepted for publication in Physics of Fluid
âNotorious RBGâ: A conversation with United States Supreme Court Justice Ruth Bader Ginsburg
On February 2, 2016, Prof. Ruth Rubio-MarĂn, Chair of Constitutional and Comparative
Public Law at the European University Institute (EUI), interviewed the U.S. Supreme Court
Associate Justice Ruth Bader Ginsburg. The interview took place in the framework of the
European University Instituteâs annual Ursula Hirschmann Lecture, a space dedicated
to stimulate research and thinking which links ideas about Europe and the study of gender.
Justice Ruth Bader Ginsburg engaged in a conversation that tackled her whole persona,
without making rigid divides between the professional and the personal. Deep legal analysis,
personal anecdotes, and invaluable advice for future researchers and lawyers intertwine in the
interview, which sheds light on important dimensions of equality law
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