Multidimensional tunneling between potential wells at non degenerate minima

We consider tunneling between symmetric wells for a 2-D semi-classical Schr\"odinger operator for energies close to the quadratic minimum of the potential V in two cases: (1) excitations of the lowest frequency in the harmonic oscillator approximation of V; (2) more general excited states from Diophantine tori with comparable quantum numbers.Comment: 6 pages, 1 figure, Conference Days on Diffraction 2014, Saint Petersburg, Russi

Asymptotics of Green function for the linear waves equations in a domain with a non-uniform bottom

We consider the linear problem for water-waves created by sources on the bottom and the free surface in a 3-D basin having slowly varying profile $z=-D(x)$. The fluid verifies Euler-Poisson equations. These (non-linear) equations have been given a Hamiltonian form by Zakharov, involving canonical variables $(\xi(x,t),\eta(x,t))$ describing the dynamics of the free surface; variables $(\xi,\eta)$ are related by the free surface Dirichlet-to-Neumann (DtN) operator. For a single variable $x\in{\bf R}$ and constant depth, DtN operator was explicitely computed in terms of a convergent series. Here we neglect quadratic terms in Zakharov equations, and consider the linear response to a disturbance of $D(x)$ harmonic in time when the wave-lenght is small compared to the depth of the basin. We solve the Green function problem for a matrix-valued DtN operator, at the bottom and the free-surface

Semi-classical Green functions

Let $H(x,p)\sim H_0(x,p)+hH_1(x,p)+\cdots$ be a semi-classical Hamiltonian on $T^*{\bf R}^n$, and $\Sigma_E=\{H_0(x,p)=E\}$ a non critical energy surface. Consider $f_h$ a semi-classical distribution (the "source") microlocalized on a Lagrangian manifold $\Lambda$ which intersects cleanly the flow-out $\Lambda_+$ of the Hamilton vector field $X_{H_0}$ in $\Sigma_E$. Using Maslov canonical operator, we look for a semi-classical distribution $u_h$ satisfying the limiting absorption principle and $H^w(x,hD_x)u_h=f_h$ (semi-classical Green kernel). In this report, we elaborate (still at an early stage) on some results announced in [Doklady Akad. Nauk, Vol. 76, No1, p.1-5, 2017] and provide some examples, in particular from the theory of wave beams.Comment: Conference Days of Diffraction 2018, St Petersbur

The role of magnetic resonance imaging in the early diagnosis of chronic lymphocytic inflammation (CLIPPERS syndrome)

Background: Chronic lymphocytic inflammation with perivascular contrast enhancement in the pons responsive to steroids (CLIPPERS) is a rare and relatively new pathology and magnetic resonance imaging (MRI) is highly important in its diagnosis. Clinical case description: The analysis of the MRI results revealed typical changes characteristic of CLIPPERS, such as contrast-positive small-point and curvilinear lesions of the pons, medulla oblongata and midbrain, as well as of the cerebral peduncles and cerebellum. In addition to the changes we described, according to the literature, lesions of the white matter of the large hemispheres and thalami may also be observed in the syndrome of chronic lymphocytic inflammation. Conclusion: MRI not only enables one to achieve high-quality neuroimaging of CLIPPERS, but also allows avoiding invasive, traumatic diagnostic methods

Brain imaging of the cortex in ADHD: a coordinated analysis of large-scale clinical and population-based samples

Objective: Neuroimaging studies show structural alterations of various brain regions in children and adults with attention deficit hyperactivity disorder (ADHD), although nonreplications are frequent. The authors sought to identify cortical characteristics related to ADHD using large-scale studies. Methods: Cortical thickness and surface area (based on the Desikan–Killiany atlas) were compared between case subjects with ADHD (N=2,246) and control subjects (N=1,934) for children, adolescents, and adults separately in ENIGMA-ADHD, a consortium of 36 centers. To assess familial effects on cortical measures, case subjects, unaffected siblings, and control subjects in the NeuroIMAGE study (N=506) were compared. Associations of the attention scale from the Child Behavior Checklist with cortical measures were determined in a pediatric population sample (Generation-R, N=2,707). Results: In the ENIGMA-ADHD sample, lower surface area values were found in children with ADHD, mainly in frontal, cingulate, and temporal regions; the largest significant effect was for total surface area (Cohen’s d=−0.21). Fusiform gyrus and temporal pole cortical thickness was also lower in children with ADHD. Neither surface area nor thickness differences were found in the adolescent or adult groups. Familial effects were seen for surface area in several regions. In an overlapping set of regions, surface area, but not thickness, was associated with attention problems in the Generation-R sample. Conclusions: Subtle differences in cortical surface area are widespread in children but not adolescents and adults with ADHD, confirming involvement of the frontal cortex and highlighting regions deserving further attention. Notably, the alterations behave like endophenotypes in families and are linked to ADHD symptoms in the population, extending evidence that ADHD behaves as a continuous trait in the population. Future longitudinal studies should clarify individual lifespan trajectories that lead to nonsignificant findings in adolescent and adult groups despite the presence of an ADHD diagnosis

Subcortical brain volume, regional cortical thickness, and cortical surface area across disorders: findings from the ENIGMA ADHD, ASD, and OCD Working Groups

Objective Attention-deficit/hyperactivity disorder (ADHD), autism spectrum disorder (ASD), and obsessive-compulsive disorder (OCD) are common neurodevelopmental disorders that frequently co-occur. We aimed to directly compare all three disorders. The ENIGMA consortium is ideally positioned to investigate structural brain alterations across these disorders. Methods Structural T1-weighted whole-brain MRI of controls (n=5,827) and patients with ADHD (n=2,271), ASD (n=1,777), and OCD (n=2,323) from 151 cohorts worldwide were analyzed using standardized processing protocols. We examined subcortical volume, cortical thickness and surface area differences within a mega-analytical framework, pooling measures extracted from each cohort. Analyses were performed separately for children, adolescents, and adults using linear mixed-effects models adjusting for age, sex and site (and ICV for subcortical and surface area measures). Results We found no shared alterations among all three disorders, while shared alterations between any two disorders did not survive multiple comparisons correction. Children with ADHD compared to those with OCD had smaller hippocampal volumes, possibly influenced by IQ. Children and adolescents with ADHD also had smaller ICV than controls and those with OCD or ASD. Adults with ASD showed thicker frontal cortices compared to adult controls and other clinical groups. No OCD-specific alterations across different age-groups and surface area alterations among all disorders in childhood and adulthood were observed. Conclusion Our findings suggest robust but subtle alterations across different age-groups among ADHD, ASD, and OCD. ADHD-specific ICV and hippocampal alterations in children and adolescents, and ASD-specific cortical thickness alterations in the frontal cortex in adults support previous work emphasizing neurodevelopmental alterations in these disorders

Short-Wave Asymptotics for Gaussian Beams and Packets and Scalarization of Equations in Plasma Physics

We study Gaussian wave beam and wave packet types of solutions to the linearized cold plasma system in a toroidal domain (tokamak). Such solutions are constructed with help of Maslov’s complex germ theory (short-wave or semi-classical asymptotics with complex phases). The term “semi-classical” asymptotics is understood in a broad sense: asymptotic solutions of evolutionary and stationary partial differential equations from wave or quantum mechanics are expressed through solutions of the corresponding equations of classical mechanics. This, in particular, allows one to use useful geometric considerations. The small parameter of the expansion is h = λ / 2 π L where λ is the wavelength and L the dimension of the system. In order to apply the asymptotic algorithm, we need this parameter to be small, so we deal only with high-frequency waves, which are in the range of lower hybrid waves used to heat the plasma. The asymptotic solution appears to be a Gaussian wave packet divided by the square root of the determinant of an appropriate Jacobi matrix (“complex divergence”). When this determinant is zero, focal points appear. Our approach allows one to write out asymptotics near focal points. We also claim that this approach is very practical and leads to formulas that can be used for numerical simulations in software like Wolfram Mathematica, Maple, etc. For the particular case of high-frequency beams, we present a recipe for constructing beams and packets and show the results of their numerical implementation. We also propose ideas to treat the more difficult general case of arbitrary frequency. We also explain the main ideas of asymptotic theory used to obtain such formulas

Occurrence of butterflies and moths (Insecta, Lepidoptera) in Mordovia State Nature Reserve

Faunistic research in protected areas is of greatest interest since these are the most unique places in the region. Many of these are islands of minimal anthropogenic impact, such as the Mordovia State Nature Reserve (Russian Federation), founded in 1936. The purpose of the publication of the basis of faunistic research - occurrences of species, is availability of factual information to a broad range of researchers and its implication in research on a wider scale.For the first time, a total of 7,606 records of Lepidoptera occurrences from the Mordovia State Nature Reserve with coordinates have been published as a dataset. It is necessary to embed them in the Global Biodiversity Information Facility (GBIF) in order to make them accessible to everyone. As a result of research from 2007 to 2021, more than 600 taxa were identified for the first time for the territory of Mordovia State Nature Reserve, including more than 450 species for the Republic of Mordovia, four species for the Middle Volga Region and eight species for the Middle and Lower Volga Region

Study of Plasma Electrolytic Oxidation Coatings on Aluminum Composites

Coatings, with a thickness of up to 75 µm, were formed by plasma electrolytic oxidation (PEO) under the alternating current electrical mode in a silicate-alkaline electrolyte on aluminum composites without additives and alloyed with copper (1–4.5%). The coatings’ structure was analyzed by scanning electron microscopy, X-ray microanalysis, X-ray photoelectron spectroscopy, nuclear backscattering spectrometry, and XRD analysis. The coatings formed for 60 min were characterized by excessive aluminum content and the presence of low-temperature modifications of alumina γ-Al2O3 and η-Al2O3. The coatings formed for 180 min additionally contained high-temperature corundum α-Al2O3, and aluminum inclusions were absent. The electrochemical behavior of coated composites and uncoated ones in 3% NaCl was studied. Alloyage of aluminum composites with copper increased the corrosion current density. Plasma electrolytic oxidation reduced it several times