1,952 research outputs found
Maximizing Neumann fundamental tones of triangles
We prove sharp isoperimetric inequalities for Neumann eigenvalues of the
Laplacian on triangular domains.
The first nonzero Neumann eigenvalue is shown to be maximal for the
equilateral triangle among all triangles of given perimeter, and hence among
all triangles of given area. Similar results are proved for the harmonic and
arithmetic means of the first two nonzero eigenvalues
Approximation of the critical buckling factor for composite panels
This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented
A free boundary problem modeling electrostatic MEMS: II. nonlinear bending effects
Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically conductive elastic membrane suspended above a fixed ground plate together with the electrostatic potential in the free domain between the membrane and the fixed ground plate. The electrostatic potential is harmonic in that domain and its values are held fixed along the membrane and the ground plate. The equation for the membrane deflection is a parabolic quasilinear fourth-order equation, which is coupled to the gradient trace of the electrostatic potential on the membrane
In situ commissioning of the ATLAS electromagnetic calorimeter with cosmic muons
In 2006, ATLAS entered the {\it in situ} commissioning phase. The primary goal of this phase is to verify the detector operation and performance with cosmic muons. Using a dedicated cosmic muon trigger from the hadronic Tile calorimeter, a sample of approximately events was collected in several modules of the barrel electromagnetic (EM) calorimeter between August 2006 and March 2007. As cosmic events are generally non-projective and arrive asynchronously with respect to the trigger clock, methods to improve the standard signal reconstruction for this situation are presented. Various selection criteria for projective muons and clustering algorithms have been tested, leading to preliminary results on calorimeter uniformity in and timing performance
Les Houches 2015: Physics at TeV colliders - new physics working group report
We present the activities of the 'New Physics' working group for the 'Physics
at TeV Colliders' workshop (Les Houches, France, 1-19 June, 2015). Our report
includes new physics studies connected with the Higgs boson and its properties,
direct search strategies, reinterpretation of the LHC results in the building
of viable models and new computational tool developments. Important signatures
for searches for natural new physics at the LHC and new assessments of the
interplay between direct dark matter searches and the LHC are also considered.Comment: Proceedings of the New Physics Working Group of the 2015 Les Houches
Workshop, Physics at TeV Colliders, Les Houches 1-19 June 2015. 197 page
Constrained and unconstrained rearrangement minimization problems related to the p-Laplace operator
In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem
−∆pu = f in D, u = 0 on ∂D.
In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also consider the case when D is a planar disk and show that the minimizer is radial and increasing. In the constrained problem we minimize the energy functional relative to the intersection of a rearrangement class with an affine subspace of codimension one in an appropriate function space. We briefly discuss our motivation for studying the constrained minimization problem
Topological and geometrical restrictions, free-boundary problems and self-gravitating fluids
Let (P1) be certain elliptic free-boundary problem on a Riemannian manifold
(M,g). In this paper we study the restrictions on the topology and geometry of
the fibres (the level sets) of the solutions f to (P1). We give a technique
based on certain remarkable property of the fibres (the analytic representation
property) for going from the initial PDE to a global analytical
characterization of the fibres (the equilibrium partition condition). We study
this analytical characterization and obtain several topological and geometrical
properties that the fibres of the solutions must possess, depending on the
topology of M and the metric tensor g. We apply these results to the classical
problem in physics of classifying the equilibrium shapes of both Newtonian and
relativistic static self-gravitating fluids. We also suggest a relationship
with the isometries of a Riemannian manifold.Comment: 36 pages. In this new version the analytic representation hypothesis
is proved. Please address all correspondence to D. Peralta-Sala
Picomolar, selective, and subtype-specific small-molecule inhibition of TRPC1/4/5 channels
The concentration of free cytosolic Ca(2+) and the voltage across the plasma membrane are major determinants of cell function. Ca(2+)-permeable non-selective cationic channels are known to regulate these parameters but understanding of these channels remains inadequate. Here we focus on Transient Receptor Potential Canonical 4 and 5 proteins (TRPC4 and TRPC5) which assemble as homomers or heteromerize with TRPC1 to form Ca(2+)-permeable non-selective cationic channels in many mammalian cell types. Multiple roles have been suggested including in epilepsy, innate fear, pain and cardiac remodeling but limitations in tools to probe these channels have restricted progress. A key question is whether we can overcome these limitations and develop tools which are high-quality, reliable, easy to use and readily accessible for all investigators. Here, through chemical synthesis and studies of native and over-expressed channels by Ca(2+) and patch-clamp assays, we describe compound 31 (C31), a remarkable small-molecule inhibitor of TRPC1/4/5 channels. Its potency ranged from 9 to 1300 pM, depending on the TRPC1/4/5 subtype and activation mechanism. Other channel types investigated were unaffected, including TRPC3, TRPC6, TRPV1, TRPV4, TRPA1, TRPM2, TRPM8 and store-operated Ca(2+) entry mediated by Orai1. These findings suggest identification of an important experimental tool compound which has much higher potency for inhibiting TRPC1/4/5 channels than previously reported agents, impressive specificity, and graded subtype selectivity within the TRPC1/4/5 channel family. The compound should greatly facilitate future studies of these ion channels. We suggest naming this TRPC1/4/5-inhibitory compound Pico145
Planck Intermediate Results. IV. The XMM-Newton validation programme for new Planck galaxy clusters
We present the final results from the XMM-Newton validation follow-up of new
Planck galaxy cluster candidates. We observed 15 new candidates, detected with
signal-to-noise ratios between 4.0 and 6.1 in the 15.5-month nominal Planck
survey. The candidates were selected using ancillary data flags derived from
the ROSAT All Sky Survey (RASS) and Digitized Sky Survey all-sky maps, with the
aim of pushing into the low SZ flux, high-z regime and testing RASS flags as
indicators of candidate reliability. 14 new clusters were detected by XMM,
including 2 double systems. Redshifts lie in the range 0.2 to 0.9, with 6
clusters at z>0.5. Estimated M500 range from 2.5 10^14 to 8 10^14 Msun. We
discuss our results in the context of the full XMM validation programme, in
which 51 new clusters have been detected. This includes 4 double and 2 triple
systems, some of which are chance projections on the sky of clusters at
different z. We find that association with a RASS-BSC source is a robust
indicator of the reliability of a candidate, whereas association with a FSC
source does not guarantee that the SZ candidate is a bona fide cluster.
Nevertheless, most Planck clusters appear in RASS maps, with a significance
greater than 2 sigma being a good indication that the candidate is a real
cluster. The full sample gives a Planck sensitivity threshold of Y500 ~ 4 10^-4
arcmin^2, with indication for Malmquist bias in the YX-Y500 relation below this
level. The corresponding mass threshold depends on z. Systems with M500 > 5
10^14 Msun at z > 0.5 are easily detectable with Planck. The newly-detected
clusters follow the YX-Y500 relation derived from X-ray selected samples.
Compared to X-ray selected clusters, the new SZ clusters have a lower X-ray
luminosity on average for their mass. There is no indication of departure from
standard self-similar evolution in the X-ray versus SZ scaling properties.
(abridged)Comment: accepted by A&
Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations
We present all-sky modelling of the high resolution Planck, IRAS, and WISE
infrared (IR) observations using the physical dust model presented by Draine
and Li in 2007 (DL). We study the performance and results of this model, and
discuss implications for future dust modelling. The present work extends the DL
dust modelling carried out on nearby galaxies using Herschel and Spitzer data
to Galactic dust emission. We employ the DL dust model to generate maps of the
dust mass surface density, the optical extinction Av, and the starlight
intensity parametrized by Umin. The DL model reproduces the observed spectral
energy distribution (SED) satisfactorily over most of the sky, with small
deviations in the inner Galactic disk and in low ecliptic latitude areas. We
compare the DL optical extinction Av for the diffuse interstellar medium with
optical estimates for 2 10^5 quasi-stellar objects (QSOs) observed in the Sloan
digital sky survey. The DL Av estimates are larger than those determined
towards QSOs by a factor of about 2, which depends on Umin. The DL fitting
parameter Umin, effectively determined by the wavelength where the SED peaks,
appears to trace variations in the far-IR opacity of the dust grains per unit
Av, and not only in the starlight intensity. To circumvent the model
deficiency, we propose an empirical renormalization of the DL Av estimate,
dependent of Umin, which compensates for the systematic differences found with
QSO observations. This renormalization also brings into agreement the DL Av
estimates with those derived for molecular clouds from the near-IR colours of
stars in the 2 micron all sky survey. The DL model and the QSOs data are used
to compress the spectral information in the Planck and IRAS observations for
the diffuse ISM to a family of 20 SEDs normalized per Av, parameterized by
Umin, which may be used to test and empirically calibrate dust models.Comment: Final version that has appeared in A&
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