3,633 research outputs found
Transference of fractional Laplacian regularity
In this note we show how to obtain regularity estimates for the fractional
Laplacian on the multidimensional torus from the fractional
Laplacian on . Though at first glance this may seem quite
natural, it must be carefully precised. A reason for that is the simple fact
that functions on the torus can not be identified with functions on
. The transference is achieved through a formula that holds in
the distributional sense. Such an identity allows us to transfer Harnack
inequalities, to relate the extension problems, and to obtain pointwise
formulas and H\"older regularity estimates.Comment: 7 pages. To appear in Special Functions, Partial Differential
Equations and Harmonic Analysis. Proceedings of the conference in honor of
Calixto P. Calder\'on, Roosevelt University at Chicago, November 16-18, 2012.
C. Georgakis, A. Stokolos and W. Urbina (eds
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
We use a characterization of the fractional Laplacian as a Dirichlet to
Neumann operator for an appropriate differential equation to study its obstacle
problem. We write an equivalent characterization as a thin obstacle problem. In
this way we are able to apply local type arguments to obtain sharp regularity
estimates for the solution and study the regularity of the free boundary
Influence of anisotropic ion shape, asymmetric valency, and electrolyte concentration on structural and thermodynamic properties of an electric double layer
Grand canonical Monte Carlo simulation results are reported for an electric
double layer modelled by a planar charged hard wall, anisotropic shape cations,
and spherical anions at different electrolyte concentrations and asymmetric
valencies. The cations consist of two tangentially tethered hard spheres of the
same diameter, . One sphere is charged while the other is neutral. Spherical
anions are charged hard spheres of diameter . The ion valency asymmetry 1:2
and 2:1 is considered, with the ions being immersed in a solvent mimicked by a
continuum dielectric medium at standard temperature. The simulations are
carried out for the following electrolyte concentrations: 0.1, 1.0 and 2.0 M.
Profiles of the electrode-ion, electrode-neutral sphere singlet distributions,
the average orientation of dimers, and the mean electrostatic potential are
calculated for a given electrode surface charge, , while the contact
electrode potential and the differential capacitance are presented for varying
electrode charge. With an increasing electrolyte concentration, the shape of
differential capacitance curve changes from that with a minimum surrounded by
maxima into that of a distorted single maximum. For a 2:1 electrolyte, the
maximum is located at a small negative value while for 1:2, at a small
positive value.Comment: 10 pages, 6 figure
Double layer for hard spheres with an off-center charge
Simulations for the density and potential profiles of the ions in the planar
electrical double layer of a model electrolyte or an ionic liquid are reported.
The ions of a real electrolyte or an ionic liquid are usually not spheres; in
ionic liquids, the cations are molecular ions. In the past, this asymmetry has
been modelled by considering spheres that are asymmetric in size and/or valence
(viz., the primitive model) or by dimer cations that are formed by tangentially
touching spheres. In this paper we consider spherical ions that are asymmetric
in size and mimic the asymmetrical shape through an off-center charge that is
located away from the center of the cation spheres, while the anion charge is
at the center of anion spheres. The various singlet density and potential
profiles are compared to (i) the dimer situation, that is, the constituent
spheres of the dimer cation are tangentially tethered, and (ii) the standard
primitive model. The results reveal the double layer structure to be
substantially impacted especially when the cation is the counterion. As well as
being of intrinsic interest, this off-center charge model may be useful for
theories that consider spherical models and introduce the off-center charge as
a perturbation.Comment: 11 pages, 7 figure
Joint constraints on galaxy bias and through the N-pdf of the galaxy number density
We present a full description of the N-probability density function of the
galaxy number density fluctuations. This N-pdf is given in terms, on the one
hand, of the cold dark matter correlations and, on the other hand, of the
galaxy bias parameter. The method relies on the assumption commonly adopted
that the dark matter density fluctuations follow a local non-linear
transformation of the initial energy density perturbations. The N-pdf of the
galaxy number density fluctuations allows for an optimal estimation of the bias
parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if
there exists any a priori information on the bias parameter), and of those
parameters defining the dark matter correlations, in particular its amplitude
(). It also provides the proper framework to perform model selection
between two competitive hypotheses. The parameters estimation capabilities of
the N-pdf are proved by SDSS-like simulations (both ideal log-normal
simulations and mocks obtained from Las Damas simulations), showing that our
estimator is unbiased. We apply our formalism to the 7th release of the SDSS
main sample (for a volume-limited subset with absolute magnitudes ). We obtain and , for galaxy number density fluctuations in cells of a size of
Mpc. Different model selection criteria show that galaxy biasing is
clearly favoured.Comment: 25 pages, 9 figures, 2 tables. v2: Substantial revision, adding the
joint constraints with \sigma_8 and testing with Las Damas mocks. Matches
version accepted for publication in JCA
The few-body problem in terms of correlated gaussians
In their textbook, Suzuki and Varga [Y. Suzuki and K. Varga, {\em Stochastic
Variational Approach to Quantum-Mechanical Few-Body Problems} (Springer,
Berlin, 1998)] present the stochastic variational method in a very exhaustive
way. In this framework, the so-called correlated gaussian bases are often
employed. General formulae for the matrix elements of various operators can be
found in the textbook. However the Fourier transform of correlated gaussians
and their application to the management of a relativistic kinetic energy
operator are missing and cannot be found in the literature. In this paper we
present these interesting formulae. We give also a derivation for new
formulations concerning central potentials; the corresponding formulae are more
efficient numerically than those presented in the textbook.Comment: 10 page
High-Resolution N2 Adsorption Isotherms at 77.4 K: Critical Effect of the He Used During Calibration
Accurate characterization of the microporous structure in porous solids is of paramount importance for several applications such as energy and gas storage, nanoconfinement reactions, and so on. Among the different techniques for precise textural characterization, high-precision gas adsorption measurement of probe molecules at cryogenic temperatures (e.g., N2 at 77.4 K and Ar at 87.3 K) is the most widely used, after appropriate calibration of the sample holder with a probe gas, which does not experience physisorption processes. Although traditionally helium has been considered not to be adsorbed in porous solids at cryogenic temperatures, here we show that even at 77.4 K (high above its boiling temperature, 4 K) the use of He in the calibration step can give rise to erroneous interpretations when narrow micropores/constrictions are present.Authors acknowledge financial support from the MICINN (project PLE2009-0052) and Generalitat Valenciana (PROMETEO/2009/002)
Faddeev approach to confined three-quark problems
We propose a method that allows for the efficient solution of the three-body
Faddeev equations in the presence of infinitely rising confinement
interactions. Such a method is useful in calculations of nonrelativistic and
especially semirelativistic constituent quark models. The convergence of the
partial wave series is accelerated and possible spurious contributions in the
Faddeev components are avoided. We demonstrate how the method works with the
example of the Goldstone-boson-exchange chiral quark model for baryons.Comment: 6 page
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