Recovering piecewise smooth functions from nonuniform Fourier measurements

In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and piecewise polynomials of fixed degree, and quadratic for piecewise polynomials of varying degree

Soft disks in a narrow channel

The pressure components of "soft" disks in a two dimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the two-body potential, u(r), is singular at some distance r_0, the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r_0. In channels with periodic boundary conditions and for potentials which are discontinuous at r_0, the transverse and longitudinal pressure components exhibit a 1/2 and 3/2 singularity, respectively. Continuous potentials with a power law singularity result in weaker singularities of the pressure components. In channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries

Model fluid in a porous medium: results for a Bethe lattice

We consider a lattice gas with quenched impurities or `quenched-annealed binary mixture' on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the 3 main factors of fluids in random porous media: wetting, randomness and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.Comment: 13 pages, 12 figure

Child sexual abuse material in child-centred institutions: situational crime prevention approaches

This paper focuses on the potential for child-centred institutions to use situational crime prevention (SCP) strategies to prevent or reduce child sexual abuse material (CSAM)1 offending as a distinct form of child sexual abuse (CSA). We discuss the failure of the Royal Commission into Institutional Responses to Child Sexual Abuse in Australia to address the potential for CSAM offending to occur in child-centred institutions. Our premise is that CSAM offending is markedly shaped by the situation in which it occurs, rather than by any pre-existing preparedness to offend sexually against children. In this context, SCP for CSAM offending must be considered as part of overall strategies to combat CSA in institutional settings. However, we acknowledge that effective implementation of SCP in this area is not straightforward. We consider some of the challenges in implementing SCP at an institutional level

Lattice-gas Monte Carlo study of adsorption in pores

A lattice gas model of adsorption inside cylindrical pores is evaluated with Monte Carlo simulations. The model incorporates two kinds of site: (a line of) ``axial'' sites and surrounding ``cylindrical shell'' sites, in ratio 1:7. The adsorption isotherms are calculated in either the grand canonical or canonical ensembles. At low temperature, there occur quasi-transitions that would be genuine thermodynamic transitions in mean-field theory. Comparison between the exact and mean-field theory results for the heat capacity and adsorption isotherms are provided

A Mass Matrix for Atmospheric, Solar, and LSND Neutrino Oscillations

We construct a mass matrix for the four neutrino flavors, three active and one sterile, needed to fit oscillations in all three neutrino experiments: atmospheric, solar, and LSND, simultaneously. It organizes the neutrinos into two doublets whose central values are about 1 eV apart, and whose splittings are of the order of 10^(-3) eV. Atmospheric neutrino oscillations are described as maximal mixing within the upper doublet, and solar as the same within the lower doublet. Then LSND is a weak transition from one doublet to the other. We comment on the Majorana versus Dirac nature of the active neutrinos and show that our mass matrix can be derived from an S_2 x S_2 permutation symmetry plus an equal splitting rule.Comment: 4 pages, 0 figures, minor text change

Rich polymorphism of a rod-like liquid crystal (8CB) confined in two types of unidirectional nanopores

We present a neutron and X-rays scattering study of the phase transitions of 4-n-octyl-4'-cyanobiphenyl (8CB) confined in unidirectional nanopores of porous alumina and porous silicon (PSi) membranes with an average diameter of 30 nm. Spatial confinement reveals a rich polymorphism, with at least four different low temperature phases in addition to the smectic A phase. The structural study as a function of thermal treatments and conditions of spatial confinement allows us to get insights into the formation of these phases and their relative stability. It gives the first description of the complete phase behavior of 8CB confined in PSi and provides a direct comparison with results obtained in bulk conditions and in similar geometric conditions of confinement but with reduced quenched disorder effects using alumina anopore membranesComment: Accepted in EPJ E - Soft Matte

Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid

When a phase-separated binary ($A+B$) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle $\theta$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, $\theta$ is estimated from the inclination of the interfaces, as a function of the wall-fluid interaction strength. The information on the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ are obtained independently from a new thermodynamic integration method, while $\gamma_{AB}$ is found from the finite-size scaling analysis of the concentration distribution function. We show that Young's equation describes the contact angles of the actual nanoscale interfaces for this model rather accurately and location of the (first order) wetting transition is estimated.Comment: 6 pages, 6 figure

Adsorption in non interconnected pores open at one or at both ends: A reconsideration of the origin of the hysteresis phenomenon

We report on an experimental study of adsorption isotherme of nitrogen onto porous silicon with non interconnected pores open at one or at both ends in order to check for the first time the old (1938) but always current idea based on Cohan's description which suggests that the adsorption of gaz should occur reversibly in the first case and irreversibly in the second one. Hysteresis loops, the shape of which is usually associated to interconnections in porous media, are observed whether the pores are open at one or at both ends in contradiction with Cohan's model.Comment: 5 pages, 4 EPS figure