Higher Dimensional Coulomb Gases and Renormalized Energy Functionals

We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n (mean-field scaling). By a suitable splitting of the Hamiltonian, we extract the next to leading order term in the ground state energy, beyond the mean-field limit. We show that this next order term, which characterizes the fluctuations of the system, is governed by a new "renormalized energy" functional providing a way to compute the total Coulomb energy of a jellium (i.e. an infinite set of point charges screened by a uniform neutralizing background), in any dimension. The renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale, as in Onsager's lemma. We obtain consequences for the statistical mechanics of the Coulomb gas: next to leading order asymptotic expansion of the free energy or partition function, characterizations of the Gibbs measures, estimates on the local charge fluctuations and factorization estimates for reduced densities. This extends results of Sandier and Serfaty to dimension higher than two by an alternative approach.Comment: Structure has slightly changed, details and corrections have been added to some of the proof

Boundary Behavior of the Ginzburg-Landau Order Parameter in the Surface Superconductivity Regime

We study the 2D Ginzburg-Landau theory for a type-II superconductor in an applied magnetic field varying between the second and third critical value. In this regime the order parameter minimizing the GL energy is concentrated along the boundary of the sample and is well approximated to leading order by a simplified 1D profile in the direction perpendicular to the boundary. Motivated by a conjecture of Xing-Bin Pan, we address the question of whether this approximation can hold uniformly in the boundary region. We prove that this is indeed the case as a corollary of a refined, second order energy expansion including contributions due to the curvature of the sample. Local variations of the GL order parameter are controlled by the second order term of this energy expansion, which allows us to prove the desired uniformity of the surface superconductivity layer

Local Density Approximation for Almost-Bosonic Anyons

We discuss the average-field approximation for a trapped gas of non-interacting anyons in the quasi-bosonic regime. In the homogeneous case, i.e., for a confinement to a bounded region, we prove that the energy in the regime of large statistics parameter, i.e., for "less-bosonic" anyons, is independent of boundary conditions and of the shape of the domain. When a non-trivial trapping potential is present, we derive a local density approximation in terms of a Thomas-Fermi-like model.Comment: Contribution to the proceedings of QMath13: Mathematical Results in Quantum Physics, 8-11 October 2016, Atlanta, U

Vortex Phases of Rotating Superfluids

We report on the first mathematically rigorous proofs of a transition to a giant vortex state of a superfluid in rotating anharmonic traps. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and large rotational velocity and is based on precise asymptotic estimates on the ground state energy. An interesting aspect is a significant difference between 'soft' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary. In the former case vortices persist in the bulk until the width of the annulus becomes comparable to the size of the vortex cores. In the second case the transition already takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus. Moreover, the density profiles in the annulus are different in the two cases. In both cases rotational symmetry of the density in a true ground state is broken, even though a symmetric variational ansatz gives an excellent approximation to the energy.Comment: For the Proceedings of 21st International Laser Physics Workshop, Calgary, July 23-27, 201

Higher Dimensional Coulomb Gases and Renormalized Energy Functionals

Structure has slightly changed, details and corrections have been added to some of the proofs.We consider a classical system of n charged particles in an external confining potential, in any dimension d larger than 2. The particles interact via pairwise repulsive Coulomb forces and the coupling parameter scales like the inverse of n (mean-field scaling). By a suitable splitting of the Hamiltonian, we extract the next to leading order term in the ground state energy, beyond the mean-field limit. We show that this next order term, which characterizes the fluctuations of the system, is governed by a new "renormalized energy" functional providing a way to compute the total Coulomb energy of a jellium (i.e. an infinite set of point charges screened by a uniform neutralizing background), in any dimension. The renormalization that cuts out the infinite part of the energy is achieved by smearing out the point charges at a small scale, as in Onsager's lemma. We obtain consequences for the statistical mechanics of the Coulomb gas: next to leading order asymptotic expansion of the free energy or partition function, characterizations of the Gibbs measures, estimates on the local charge fluctuations and factorization estimates for reduced densities. This extends results of Sandier and Serfaty to dimension higher than two by an alternative approach

PENGARUH INTENSITAS KOMUNIKASI DENGAN APLIKASI LINE DAN FREKUENSI PENGGUNAAN STIKER PADA APLIKASI LINE TERHADAP EFEKTIFITAS KOMUNIKASI INTERPERSONAL

Aplikasi LINE merupakan salah satu media dalam menyampaikan pesan. Pesan dalam aplikasi LINE dapat dikirim maupun diterima dengan lebih mendalam karena memiliki fitur media audio dan visual seperti stiker, pesan suara, dan pesan video. Penelitian ini menggunakan beberapa teori seperti teori komunikasi interpersonal, dan teori efektifitas. Penelitian ini bertujuan untuk mengetahui hubungan antara Intensitas Komunikasi dengan Aplikasi LINE terhadap efektifitas komunikasi interpersonal, lalu hubungan Frekuensi Penggunaan Stiker pada Aplikasi LINE terhadap Efektifitas Komunikasi Interpersonal, serta pengaruh dan hubungan keduanya terhadap efektifitas komunikasi interpersonal. Penelitian ini berjenis penelitian kuantitatif yang menggunakan metode korelasional yang dilakukan pada mahasiswa dan mahasiswi Program Studi Ilmu Komunikasi Fakultas Ilmu Sosial dan Politik Universitas Sebelas Maret Surakarta Angkatan 2014 dan 2015, dengan populasi sebanyak 156 orang dan 61 orang diantaranya menjadi sampel dengan teknik sampling acak sederhana. Data pada penelitian ini dikumpulkan dengan metode penyebaran kuesioner, lalu diolah dan dianalisis menggunakan analisis korelasional Spearman serta analisis regresi linier berganda. Berdasarkan hasil penelitian, dapat diketahui variabel Intensitas Komunikasi dengan Aplikasi LINE dan variabel penggunaan stiker pada aplikasi LINE memiliki hubungan yang kuat terhadap variabel efektifitas komunikasi interpersonal, lalu kedua variabel tersebut memiliki pengaruh yang positif terhadap variabel efektifitas komunikasi interpersonal. Semakin tinggi intensitas komunikasi dengan aplikasi LINE dan penggunaan stiker pada aplikasi LINE, maka semakin tinggi pula efektifitas komunikasi interpersonal. Kata Kunci: LINE, Intensitas Komunikasi, Efektifitas Komunikasi Interpersona

How do general practitioners put preventive care recommendations into practice? A cross-sectional study in Switzerland and France.

We previously identified that general practitioners (GPs) in French-speaking regions of Europe had a variable uptake of common preventive recommendations. In this study, we describe GPs' reports of how they put different preventive recommendations into practice. Cross-sectional study conducted in 2015 in Switzerland and France. 3400 randomly selected GPs were asked to complete a postal (n=1100) or online (n=2300) questionnaire. GPs who exclusively practiced complementary and alternative medicine were not eligible for the study. 764 GPs (response rate: postal 47%, online 11%) returned the questionnaire (428 in Switzerland and 336 in France). We investigated how the GPs performed five preventive practices (screening for dyslipidaemia, colorectal and prostate cancer, identification of hazardous alcohol consumption and brief intervention), examining which age group they selected, the screening frequency, the test they used, whether they favoured shared decision for prostate cancer screening and their definition of hazardous alcohol use. A large variability was observed in the way in which GPs provide these practices. 41% reported screening yearly for cholesterol, starting and stopping at variable ages. 82% did not use any test to identify hazardous drinking. The most common responses for defining hazardous drinking were, for men, ≥21 drinks/week (24%) and ≥4 drinks/occasion for binge drinking (20%), and for women, ≥14 drinks/week (28%) and ≥3 drinks/occasion (21%). Screening for colorectal cancer, mainly with colonoscopy in Switzerland (86%) and stool-based tests in France (93%), was provided every 10 years in Switzerland (65%) and 2 years in France (91%) to patients between 50 years (87%) and 75 years (67%). Prostate cancer screening, usually with shared decision (82%), was provided yearly (62%) to patients between 50 years (74%) and 75-80 years (32%-34%). The large diversity in the way these practices are provided needs to be addressed, as it could be related to some misunderstandingof the current guidelines, to barriers for guideline uptake or, more likely, to the absence of agreement between the various recommendations

Vortex Rings in Fast Rotating Bose-Einstein Condensates

When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex phase appears, that is the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii energy on the unit disc. In particular we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold there are vortices in the condensate. We prove that they gather along a particular circle on which they are evenly distributed. This is done by providing new upper and lower bounds to the GP energy.Comment: to appear in Archive of Rational Mechanics and Analysi

Australian Sphingidae – DNA Barcodes Challenge Current Species Boundaries and Distributions

© 2014 Rougerie et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate

We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps \to 0 with the angular velocity $\Omega$ proportional to (\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0 (\eps^2|\log\eps|)^{-1} and $\Omega_0 > 2(3\pi)^{-1}$ then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk of the mass. The vorticity resides in a complementary `hole' around the center where the density is vanishingly small. Moreover, we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To be published in Commun. Math. Phy