Dissipation anomaly and energy cascade in 3D incompressible flows

The purpose of this note is to present a mathematical evidence of dissipation anomaly in 3D turbulent flows within a general setting for the study of energy cascade in physical scales of 3D incompressible flows recently introduced by the authors.Comment: accepted to C. R. Math. Acad. Sci. Paris, final versio

Anomalous dissipation and energy cascade in 3D inviscid flows

Adopting the setting for the study of existence and scale locality of the energy cascade in 3D viscous flows in physical space recently introduced by the authors to 3D inviscid flows, it is shown that the anomalous dissipation is -- in the case of decaying turbulence -- indeed capable of triggering the cascade which then continues ad infinitum, confirming Onsager's predictions.Comment: 14 pages, 1 figure, accepted to Comm. Math. Phy

Coherent vortex structures and 3D enstrophy cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities - 1/2-H\"older coherence of the vorticity direction - coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.Comment: 15 pp; final version -- to appear in CM

Management of the soft tissues of head and neck after dog bites at children

Department of Pediatric Surgery, Orthopedics and Anesthesiology Nicolae Testemitanu State University of Medicine and Pharmacy, Chisinau, Republic of Moldova, The 8th International Medical Congress for Students and Young Doctors, September 24-26, 2020Background. Even though the injuries of head and neck are mostly produced after car accidents( in 80% of cases), dog bites which are 90% of all animal bites are frequent at children. Bite wounds have always been considered complex injuries contaminated with unique polymicrobial inoculum. Because wounds of the extremities constitute the majority of bite cases, most relevant studies have focused on the wound infections rate in these areas. However, a substantial subset of dog bites are located on the face, where fear of potential disfigurment is a concern and the associated psychological consequences can be devastating. (K,Stefanopoulos). 25% of the victims of dog bites are under age 6, and 34% are aged 6 to 17. In small children, most bite wounds are on the head and neck; in older children and adolescents, most are on the limbs. There have been estimated a total of 44,000 facial wounds due to dog bites each year in the USA. In the Republic of Moldova there is also a significant number of 740 to 100,000 persons, which is three times less then the real number of dog bites wounds. The injuries that result after these bites need a complex treatment and hospitalization. There is a large range of lesions and infectious complications that can result after dog bites, therefore studying the surgical methods and the complex pharmaceutical treatment is of a paramount importance. The interdisciplinary management is recommended in dog bites inflected to the head and neck at children. The antibiotic prophylaxis is used only in high risk of infection, depending on the type, localization, animal species and patient characteristics. Many of bites appear at children that are familiar to the dogs that attack them, therefore knowing the epidemiology of them(scientific support, provocation, type of injury, risk factors)could help in spreading the information to parents, teachers and the general public to understand the behavior of dogs over the vulnerable persons. Case report. Patient X, male, 3 years. Diagnosis: Multiple injuries in the head and neck region with tissue defect of 2/3 in the skin part of the head in occipital parietal front with cortical exposure. Treatment: 1. Primary surgical treatment 2. Boring of cortical in the occipital parietal front for stimulating the granulation tissue 3. Revision and extension of the wholes for stimulating the granulation tissue 4. Grafting the granulated wounds of the head with split grafts 5. Excision of skin for grafting 6. Split skin grafts on small granulated zones 7. Excision of skin for grafting 8. Wound dressing 9. Debridement of skin and subcutaneous tissue 10. Treatment in resuscitation / intensive care the evolution of the disease with improvement. No particularities. The patient's condition upon discharge is satisfactory. Internment date: 20th of September 2019 Discharge date: 24th of November 2019 Conclusions. 1. Due to the small stature of the children up to 5 years, most of the injuries resulting from the aggression of the dogs return to the level of the head and neck. The traumatic lesions of the given region represent a surgical emergency due to the localization of organs with vital functions such as the eyes, nose, mouth, ears, etc. but also to the aesthetic aspect of the Maxillofacial region. 2. One of the most effective methods of restoring the massive defects of the scalp after dog bites in children is the exposure of the diploid by multiple trepidation of the scalp. After about 4 weeks the granulation tissue from the holes begins to cover the defect, forming a favorable vascular bed for the skin grafts. 3. Dog bites management should include measures to ensure wound care as close as possible to the accident. These actions should be directed towards identifying and minimizing the risk of infection or other serious complications. Surgical treatment includes general measures of local therapy, as well as antiinfectious prophylaxis. Interdisciplinary collaboration is recommended to ensure the best aesthetic and functional result. 4. Implementing prevention strategies (educating owners and training dogs, monitoring threatening behavior and tackling future safety measures) can be helpful in developing policy that can reduce this type of preventable trauma

Backward time behavior of dissipative PDE

We study behavior for negative times t of the 2D periodic Navier-Stokes equations and Burgers' original model for turbulence. Both systems are proved to have rich sets of solutions that exist for all t - R and increase exponentially as t -> -(Infinity) However, our study shows that the behavior of these solutions as well as the geometrical structure of the sets of their initial data are very different. As a consequence, Burgers original model for turbulence becomes the first known dissipative system that despite possessing a rich set of backward-time exponentially growing solutions, does not display any similarities, as t -> -(Infinity), to the linear case