A dyadic model on a tree

We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It mimics 3d Euler and Navier-Stokes equations in a rough approximation of a wavelet decomposition. We prove existence of finite energy solutions, anomalous dissipation in the inviscid unforced case, existence and uniqueness of stationary solutions (either conservative or not) in the forced case

Stochastic Navier-Stokes Equations and Related Models

Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier-Stokes equations, J. Math. Pures Appl., 2003), is reviewed focusing on 3D Navier-Stokes equations and dyadic models of turbulence

The impact of white noise on a supercritical bifurcation in the Swift-Hohenberg equation

We consider the impact of additive Gaussian white noise on a supercritical pitchfork bifurcation in an unbounded domain. As an example we focus on the stochastic Swift-Hohenberg equation with polynomial nonlinearity. Here we identify the order where small noise first impacts the bifurcation. Using an approximation via modulation equations, we provide a tool to analyse how the noise influences the dynamics close to a change of stability.Comment: To appear on Physica D: Nonlinear Phenomen

Limits of stochastic Volterra equations driven by Gaussian noise

We study stochastic Volterra equations in Hilbert spaces driven by cylindrical Gaussian noise. We derive a mild formulation for the stochastic Volterra equation, prove the equivalence of mild and strong solutions, the existence and uniqueness of mild solutions, and study space-time regularity. Furthermore, we establish the stability of mild solutions in $L^q(\R_+)$, prove the existence of limit distributions in the Wasserstein $p$-distance with $p \in [1,\infty)$, and characterise when these limit distributions are independent of the initial state of the process despite the presence of memory. While our techniques allow for a general class of Volterra kernels, they are particularly suited for completely monotone kernels and fractional Riemann-Liouville kernels in the full range $\alpha \in (0,2)$

Processi di Dirichlet e applicazioni

In questa tesi definiamo e costruiamo il processo di Dirichlet. Dopo averne presentate le principali proprietà, anche attraverso costruzioni alternative, studiamo due possibili applicazioni. La prima è la costruzione della misura entropica sullo spazio delle misure di probabilità su una varietà riemanniana, in particolare nel caso unidimensionale. La seconda è la proposta di un modello probabilistico per la previsione spaziale delle eruzioni in una zona vulcanicamente attiva. Come caso di studio presentiamo i Campi Flegrei

Facial Mobility after Maxilla-Mandibular Advancement in Patients with Severe Obstructive Sleep Apnea Syndrome: A Three-Dimensional Study

Introduction. The functional results of surgery in terms of facial mobility are key elements in the treatment of patients. Little is actually known about changes in facial mobility following surgical treatment with maxillomandibular advancement (MMA). Objectives. The three-dimensional (3D) methods study of basic facial movements in typical OSAS patients treated with MMA was the topic of the present research. Materials and Methods. Ten patients affected by severe obstructive sleep apnea syndrome (OSAS) were engaged for the study. Their facial surface data was acquired using a 3D laser scanner one week before (T1) and 12 months after (T2) orthognathic surgery. The facial movements were frowning, grimace, smiling, and lip purse. They were described in terms of surface and landmark displacements (mm). The mean landmark displacement was calculated for right and left sides of the face, at T1 and at T2. Results. One year after surgery, facial movements were similar to presurgical registrations. No modifications of symmetry were present. Conclusions. Despite the skeletal maxilla-mandible expansion, orthognathic surgical treatment (MMA) of OSAS patients does not seem to modify facial mobility. Only an enhancement of amplitude in smiling and knitting brows was observed. These results could have reliable medical and surgical applications

A Comparison of Times Taken for the Placement of the First portal and Complication Rates between the Veress Needle Technique and the Modified Hasson Technique in Canine Ovariectomy Laparoscopic Surgery

Minimally invasive surgery is increasingly being used in veterinary medicine. Laparoscopic procedures have several advantages compared with open surgery. These include the magnification of the field of surgery, reduced post-surgical pain and associated stress, reduced post-operative infection rates, and decreased hospitalization time. The establishment of a pneumoperitoneum is a critical step; however, this procedure can prolong the operation time, and most of the complications associated with laparoscopic surgery have been attributed to the insertion of devices into the abdominal cavity. Two main techniques have been employed to create pneumoperitoneum: the closed-entry method using the Veress needle and the open Hasson technique. The first portal is necessary to start insufflation and, subsequently, to realize the operative channel to insert the laparoscopic instruments into the abdomen. Many authors have compared the time necessary to create the first portal using different techniques in human medicine, but studies on this topic in veterinary medicine are lacking. In the veterinary medicine literature, complications associated with the creation of a pneumoperitoneum and the placement of ports include spleen, bowel, or bladder injuries; pneumothorax; and subcutaneous emphysema. The aim of the present study was to compare the times required for the placement of the first portal and the creation of pneumoperitoneum, and the rates of intraoperative complications using the Veress needle technique (VNT) and the open modified Hasson technique (MHT). The sample population comprised 30 female dogs who underwent laparoscopic ovariectomies. The dogs were randomly organized into two groups and two different entry techniques were used: Veress needle (VNT = group A) and the modified Hasson technique (MHT = group B). Complications related to abdominal entry were classified as major, in cases of organ perforation, and minor, in cases of subcutaneous emphysema and gas leakage. The VNT and MHT required 374.0 s and 242.9 s, respectively, for the placement of the first portal and for establishing pneumoperitoneum (p < 0.05). Their major complications rates were 20% and 0%, respectively (p < 0.05). Their minor complications rates were 20% and 35%, respectively (p < 0.05). No surgical procedures required laparotomy. The MHT was associated with a lower major complication rate and required less time to create the first portal, compared with the Veress needle technique