Asymptotic Analysis of the Eigenvalues of a Laplacian Problem in a Thin Multidomain

We consider a thin multidomain of $R^N$, N>1, consisting of two vertical cylinders, one placed upon the other: the first one with given height and small cross section, the second one with small thickness and given cross section. In this multidomain we study the asymptotic behavior, when the volumes of the two cylinders vanish, of a Laplacian eigenvalue problem and of a $L^2$-Hilbert orthonormal basis of eigenvectors. We derive the limit eigenvalue problem (which is well posed in the union of the limit domains, with respective dimension 1 and N-1) and the limit basis. We discuss the limit models and we precise how these limits depend on the dimension N and on limit of the ratio between the volumes of the two cylinders

Junction of elastic plates and beams (Preliminary version)

We consider the linearized elasticity system in a multidomain of the three dimensional space. This multidomain is the union of a horizontal plate, with fixed cross section and small thickness "h", and of a vertical beam with fixed height and small cross section of radius "r". The lateral boundary of the plate and the top of the beam are assumed to be clamped. When "h" and "r" tend to zero simultaneously, with "r" much greater than the square of "h", we identify the limit problem. This limit problem involves six junction conditions.Comment: Ceci est la redaction du 3 Mars 2003. Francois Murat souhaite y faire des modification

Asymptotic analysis of the high frequencies for the Laplace operator in a thin T-like shaped structure

We consider a spectral problem for the Laplacian operator in a planar T-like shaped thin structure , where E; denotes the transversal thickness of both branches. We assume the homogeneous Dirichlet boundary condition on the ends of the branches and the homogeneous Neumann boundary condition on the remaining part of the boundary of . We study the asymptotic behavior, as ; tends to zero, of the high frequencies of such a problem. Unlike the asymptotic behavior of the low frequencies where the limit problem involves only longitudinal vibrations along each branch of the T-like shaped thin structure (i.e. 1D limit spectral problems), we obtain a two dimensional limit spectral problem which allows us to capture other kinds of vibrations. We also give a characterization of the asymptotic form of the eigenfunctions originating these vibrations.This work has partially been supported by MINECO grant MTM2013-44883-P and MICINN grant PGC2018-098178-B-I00. The first author is also member of the Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM)

Junction of elastic plates and beams (Preliminary version)

Ceci est la rédaction du 3 Mars 2003. François Murat souhaite y faire des modifications.We consider the linearized elasticity system in a multidomain of the three dimensional space. This multidomain is the union of a horizontal plate, with fixed cross section and small thickness "h", and of a vertical beam with fixed height and small cross section of radius "r". The lateral boundary of the plate and the top of the beam are assumed to be clamped. When "h" and "r" tend to zero simultaneously, with "r" much greater than the square of "h", we identify the limit problem. This limit problem involves six junction conditions

P3‐145: HEREDITARY SPASTIC PARAPLEGIA AND ALZHEIMER'S DISEASE: CLINICAL AND GENETIC STUDY OF A BRAZILIAN FAMILY

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KIAA1840 mutations cause ARCMT2

Charcot–Marie–Tooth disease is a group of hereditary peripheral neuropathies that share clinical characteristics of progressive distal muscle weakness and atrophy, foot deformities, distal sensory loss, as well as diminished tendon reflexes. Hundreds of causative DNA changes have been found, but much of the genetic basis of the disease is still unexplained. Mutations in the ALS5/SPG11/ KIAA1840 gene are a frequent cause of autosomal recessive hereditary spastic paraplegia with thin corpus callosum and peripheral axonal neuropathy, and account for ∼40% of autosomal recessive juvenile amyotrophic lateral sclerosis. The overlap of axonal Charcot–Marie–Tooth disease with both diseases, as well as the common autosomal recessive inheritance pattern of thin corpus callosum and axonal Charcot–Marie–Tooth disease in three related patients, prompted us to analyse the ALS5/SPG11/ KIAA1840 gene in affected individuals with autosomal recessive axonal Charcot–Marie–Tooth disease. We investigated 28 unrelated families with autosomal recessive axonal Charcot–Marie–Tooth disease defined by clinical, electrophysiological, as well as pathological evaluation. Besides, we screened for all the known genes related to axonal autosomal recessive Charcot–Marie-Tooth disease (CMT2A2/HMSN2A2/ MFN2 , CMT2B1/ LMNA , CMT2B2/ MED25 , CMT2B5/ NEFL , ARCMT2F/dHMN2B/ HSPB1 , CMT2K/ GDAP1 , CMT2P/ LRSAM1 , CMT2R/ TRIM2 , CMT2S/ IGHMBP2 , CMT2T/ HSJ1 , CMTRID/ COX6A1 , ARAN-NM/ HINT and GAN/ GAN ), for the genes related to autosomal recessive hereditary spastic paraplegia with thin corpus callosum and axonal peripheral neuropathy (SPG7/ PGN , SPG15/ ZFYVE26, SPG21/ ACP33 , SPG35/ FA2H , SPG46/ GBA2 , SPG55/ C12orf65 and SPG56/ CYP2U1 ), as well as for the causative gene of peripheral neuropathy with or without agenesis of the corpus callosum ( SLC12A6 ) . Mitochondrial disorders related to Charcot–Marie–Tooth disease type 2 were also excluded by sequencing POLG and TYMP genes. An additional locus for autosomal recessive Charcot–Marie–Tooth disease type 2H on chromosome 8q13-21.1 was excluded by linkage analysis. Pedigrees originated in Italy, Brazil, Canada, England, Iran, and Japan. Interestingly, we identified 15 ALS5/SPG11/ KIAA1840 mutations in 12 families (two sequence variants were never reported before, p.Gln198* and p.Pro2212fs*5). No large deletions/duplications were detected in these patients. The novel mutations seemed to be pathogenic since they co-segregated with the disease in all pedigrees and were absent in 300 unrelated controls. Furthermore, in silico analysis predicted their pathogenic effect. Our results indicate that ALS5/SPG11/ KIAA1840 is the causative gene of a wide spectrum of clinical features, including autosomal recessive axonal Charcot–Marie–Tooth disease

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements