Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\gamma \in [0,1)$ and satisfy $K(x,y) \leq C (x^{\gamma} + y^{\gamma})$. More precisely, for any $\rho \in (\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\rho)}$ as $x \to \infty$

Asymptotics of self-similar solutions to coagulation equations with product kernel

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel $K(\xi,\eta)= (\xi \eta)^{\lambda}$ with $\lambda \in (0,1/2)$. It is known that such self-similar solutions $g(x)$ satisfy that $x^{-1+2\lambda} g(x)$ is bounded above and below as $x \to 0$. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function $h(x)=h_{\lambda} x^{-1+2\lambda} g(x)$ in the limit $\lambda \to 0$. It turns out that $h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)$ as $x \to 0$. As $x$ becomes larger $h$ develops peaks of height $1/\lambda$ that are separated by large regions where $h$ is small. Finally, $h$ converges to zero exponentially fast as $x \to \infty$. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE

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

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 = <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)

Probing the role of Nd3+ ions in the weak multiferroic character of NdMn2O5 by optical spectroscopies

Raman and infrared spectroscopies are used as local probes to study the dynamics of the Nd-O bonds in the weakly multiferroic NdMn2O5 system. The temperature dependence of selected Raman excitations reveals the splitting of the Nd-O bonds in NdMn2O5. The Nd3+ ion crystal field (CF) excitations in NdMn2O5 single crystals are studied by infrared transmission as a function of temperature, in the 1800-8000 cm-1 range, and under an applied magnetic field up to 11 T. The frequencies of all 4Ij crystal-field levels of Nd3+ are determined. We find that the degeneracy of the ground-state Kramers doublet is lifted ({\Delta}0 ~7.5 cm-1) due to the Nd3+-Mn3+ interaction in the ferroelectric phase, below TC ~ 28 K. The Nd3+ magnetic moment mNd(T) and its contribution to the magnetic susceptibility and the specific heat are evaluated from {\Delta}0(T) indicating that the Nd3+ ions are involved in the magnetic and the ferroelectric ordering observed below ~ 28 K. The Zeeman splitting of the excited crystal field levels of the Nd3+ ions at low temperature is also analyzed.Comment: This paper is accepted for publication as a Regular Article in Physical Review

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

A sequential data assimilation approach for the joint reconstruction of mantle convection and surface tectonics

International audienceWith the progress of mantle convection modelling over the last decade, it now becomes possible to solve for the dynamics of the interior flow and the surface tectonics to first order. We show here that tectonic data (like surface kinematics and seafloor age distribution) and mantle convection models with plate-like behaviour can in principle be combined to reconstruct mantle convection. We present a sequential data assimilation method, based on suboptimal schemes derived from the Kalman filter, where surface velocities and seafloor age maps are not used as boundary conditions for the flow, but as data to assimilate. Two stages (a forecast followed by an analysis) are repeated sequentially to take into account data observed at different times. Whenever observations are available, an analysis infers the most probable state of the mantle at this time, considering a prior guess (supplied by the forecast) and the new observations at hand, using the classical best linear unbiased estimate. Between two observation times, the evolution of the mantle is governed by the forward model of mantle convection. This method is applied to synthetic 2-D spherical annulus mantle cases to evaluate its efficiency. We compare the reference evolutions to the estimations obtained by data assimilation. Two parameters control the behaviour of the scheme: the time between two analyses, and the amplitude of noise in the synthetic observations. Our technique proves to be efficient in retrieving temperature field evolutions provided the time between two analyses is 10 Myr. If the amplitude of the a priori error on the observations is large (30 per cent), our method provides a better estimate of surface tectonics than the observations, taking advantage of the information within the physics of convection

Pain Intensity in the First 96 Hours After Abdominal Surgery: A Prospective Cohort Study.

Multimodal pain management strategies aim to improve postoperative pain control. The purpose of this study was to analyze pain scores and risk factors for acute postoperative pain after various abdominal surgery procedures. Data on 11 different abdominal surgery procedures were prospectively recorded. Pain intensity (rest, mobilization) and patient satisfaction at discharge were assessed using a visual analog scale (VAS; 0-10), and analgesic consumption was recorded until 96 hours postoperation. Demographic, surgery-related, and pain management-related univariate risk factors for insufficient pain control (VAS ≥ 4) were entered in a multivariate logistic regression model. A total of 1,278 patients were included. Overall, mean VAS scores were <3 at all time points, and scores at mobilization were consistently higher than at rest (P < 0.05). Thirty percent of patients presented a prolonged VAS score ≥4 at mobilization at 24 hours, significantly higher than at rest (14%, P < 0.05). High pain scores correlated with high opioid consumption, whereas a variability of pain scores was observed in patients with low opioid consumption. The only independent risk factor for moderate and severe pain (VAS ≥ 4) was younger age (<70 years, P = 0.001). The mean satisfaction score was 8.18 ± 1.29. Among 1,278 patients, pain was controlled adequately during the first four postoperative days, resulting in high levels of patient satisfaction. Pain levels were higher at mobilization. Younger age was the only independent risk factor for insufficient pain control. Preventive treatment in patients <70 years old and before mobilization could be evaluated for potential improvement