Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked

On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other

Quantitative lower bounds for the full Boltzmann equation, Part I: Periodic boundary conditions

We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad's cutoff assumption, the lower bound is a global Maxwellian and its asymptotic behavior in velocity is optimal, whereas for non-cutoff collision kernels the lower bound we obtain decreases exponentially but faster than the Maxwellian. Our results cover solutions constructed in a spatially homogeneous setting, as well as small-time or close-to-equilibrium solutions to the full Boltzmann equation in the torus. The constants are explicit and depend on the a priori bounds on the solution.Comment: 37 page

Bi-defects of Nematic Surfactant Bilayers

We consider the effects of the coupling between the orientational order of the two monolayers in flat nematic bilayers. We show that the presence of a topological defect on one bilayer generates a nontrivial orientational texture on both monolayers. Therefore, one cannot consider isolated defects on one monolayer, but rather associated pairs of defects on either monolayer, which we call bi-defects. Bi-defects generally produce walls, such that the textures of the two monolayers are identical outside the walls, and different in their interior. We suggest some experimental conditions in which these structures could be observed.Comment: RevTeX, 4 pages, 3 figure

Gapped tunneling spectra in the normal state of Pr2−x_{2-x}Cex_xCuO4_4

We present tunneling data in the normal state of the electron doped cuprate superconductor Pr$_{2-x}$Ce$_x$CuO$_4$ for three different values of the doping $x$. The normal state is obtained by applying a magnetic field greater than the upper critical field, $H_{c2}$ for $T < T_c$. We observe an anomalous normal state gap near the Fermi level. From our analysis of the tunneling data we conclude that this is a feature of the normal state density of states. We discuss possible reasons for the formation of this gap and its implications for the nature of the charge carriers in the normal and the superconducting states of cuprate superconductors.Comment: 7 pages ReVTeX, 11 figures files included, submitted to PR

The Enskog Process

The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the system at each fixed time is shown to be unique. The existence of a probability density for the time-marginals of the velocity is verified in the case where the initial condition is Gaussian, and is shown to be the density of an invariant measure.Comment: 38 page

Field and Laboratory Investigations on the Use of Fly Ash and LI-Based Admixtures to Prevent ASR in Concrete

Since the early 1990’s, CANMET (Department of Natural Resources Canada) is carrying out a comparative field and laboratory research program to investigate the efficacy of laboratory test procedures for properly predicting the long-term efficacy of supplementary cementitious materials (SCM) in controlling expansion due to alkali-silica reaction (ASR). Binary and ternary concrete systems, i.e. fly ash (Class F), lithium-based admixtures, fly ash / Li-based admixtures, were selected with a variety of alkali-silica reactive aggregates. The expansive behaviour of the various combinations listed above was investigated in the laboratory using concrete prisms stored under accelerated test conditions (38oC and 100% RH). Exposure blocks cast from the above mixtures were placed outdoors at the CANMET facilities located in Ottawa (Canada). This paper compares the results of expansion testing in the laboratory against that of exposure blocks after 15 years outdoors. The results are also analysed in view of providing recommendations for the use of such materials / combinations for the manufacture of concrete that will be at a minimum risk of developing deleterious expansion and cracking due to ASR

Is standardized care feasible in the emergency setting? A case matched analysis of patients undergoing laparoscopic cholecystectomy.

Immediate laparoscopic cholecystectomy is the accepted standard for the treatment of acute cholecystitis. The aim of the present study was to evaluate the feasibility of a standardized approach with tailored care maps for pre- and postoperative care by comparing pain, nausea and patient satisfaction after elective and emergent laparoscopic cholecystectomy. From January 2014 until April 2015, data on pain and nausea management were prospectively recorded for all elective and emergency procedures in the department of visceral surgery. This prospective observational study compared consecutive laparoscopic elective vs. emergency cholecystectomies. Visual analogue scales (VAS) were used to measure pain, nausea, and satisfaction from recovery room until 96 hours postoperatively. Final analysis included 168 (79%) elective cholecystectomies and 44 (21%) emergent procedures. Demographics (Age, gender, BMI and ASA-scores) were comparable between the 2 groups. In the emergency group, patients did not receive anxiolytic medication (0% vs.13%, p = 0.009) and less postoperative nausea and vomiting (PONV) prophylaxis (77% vs. 97% p = &lt;0.001). Perioperative pain management was similar in terms of opioid consumption (median amount of fentanyl 450ug [IQR 350-500] vs. 450ug [375-550], p = 0.456) and wound infiltration rates (24% vs. 25%, p = 0.799). Postoperative consumption of paracetamol, metamizole and opiod medications were similar between the 2 groups. VAS scores for pain (p = 0.191) and nausea (p = 0.392) were low for both groups. Patient satisfaction was equally high in both clinical settings (VAS 8.5 ± 1.1 vs. 8.6 ± 1.1, p = 0.68). A standardized pathway allows equally successful control of pain and nausea after both elective and emergency laparoscopic cholecystectomy. This study was retrospectively registered by March 01, 2016 in the following trial register: www.researchregistry.com (UIN researchregistry993)

Azathioprine and 6-Mercaptopurine use in the Swiss IBD cohort : adverse effects, causes of discontinuation and risk of "flares" according to 6-TG levels

Background: To characterize and analyze in the Swiss IBD Cohort: a) reported Azathioprine (AZA) and 6-Mercaptopurine (6-MP) adverse effects (AE), b) causes of discontinuation and c) response to therapy according to gastroenterologists' clinical judgment, d) whether level of 6-TGN &lt; 235pmol/8 x108 red blood cells (RBC) is associated with a higher risk of "flare" occurrence. Methods: Retrospective statistical description, Cox model and Kaplan-Meier survival estimation. Results: 1499 patients with Crohn's Disease (CD) and 1066 with Ulcerative colitis (UC)