597 research outputs found
Report on the open meeting of restricted ECFA held at the University of Athens 10 February 1983
No full textThis report summarizes the opening presentation by J. Mulvey, L. Resvanis and T. Filippas, and the main points raised during the following discussion on the situation of high-energy physics in Greece
Whispering gallery modes for a transmission problem
No full textWe construct a specific family of eigenfunctions for a Laplace operator with coefficients having a jump across an interface. These eigenfunctions have an exponential concentration arbitrarily close to the interface, and therefore could be considered as whispering gallery modes. The proof is based on an appropriate Agmon estimate. We deduce as a corollary that the quantitative unique continuation result for waves propagating in singular media proved by the author in [7] is optimal
Modulation Theory for the Blowup of Vector-Valued Nonlinear Heat Equations
No full textAbstractThis paper is concerned with the blowup of solutions of the nonlinear vector-valued heat equation Ut − ΔU = |U|p − 1U, U(0) = U0, where U(x, t) = (u1(x, t), ..., um(x, t)) is a vector-valued function from Rn × (0, T) to Rm and 1 < p < (3n + 8)/(3n − 4). Working with the equation in similarity variables, and using modulation theory and ideas from center manifold theory, we obtain the asymptotic behavior of U in a backward space-time parabola near any blowup point
Quantitative unique continuation for wave operators with a jump discontinuity across an interface and applications to approximate control
No full textIn this article we prove quantitative unique continuation results for wave
operators of the form 2 t -- div(c(x)) where the
scalar coefficient c is discontinuous across an interface of codimension one in
a bounded domain or on a compact Riemannian manifold. We do not make any
assumptions on the geometry of the interface or on the sign of the jumps of the
coefficient c. The key ingredient is a local Carleman estimate for a wave
operator with discontinuous coefficients. We then combine this estimate with
the recent techniques of Laurent-L{\'e}autaud [LL19] to propagate local unique
continuation estimates and obtain a global stability inequality. As a
consequence, we deduce the cost of the approximate controllability for waves
propagating in this geometry
Location and analytics for verticals
No full textThis chapter presents the main techniques of the location-based analytics for vertical applications. First, we discuss people-centric data analytics, providing the reader with example analytics for crowd mobility and flow monitoring, as well as a case study on COVID-19 contact tracing. Then, we provide an overview on the use of location and location-based analytics for the road safety applications, by detailing the main use cases, requirements, and architectural aspects
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Search for Massive Photon Pair Production at the CERN Intersecting Storage Rings
No full textA search for massive photon pair production at ..sqrt..s = 63 GeV has been carried out on the data sample previously employed for the electron pair production study. Positive evidence is reported for m/sub ..gamma gamma../ > 6 GeV, with a production cross-section similar to Drell-Yan electron pairs. The ratio ..gamma gamma../..pi../sup 0/..pi../sup 0/ was measured to be approx. 10/sup -3/ for a p/sub T/ of each ..gamma.. or ..pi../sup 0/ above 3 GeV/c
Inclusive eta production at high p at the ISR
No full textThe inclusive eta production cross section at the CERN ISR has been measured for p/sub T/ values of up to 11 GeV/c. The authors find that the eta / pi /sup 0/ cross-section ratio has an average value of 0.55+or-0.07 and varies little with p/sub T/. (10 refs)
Duality and Integrability in Superstring and Gauge Field Theory
No full textIn the present thesis, we explore certain aspects of superstring and supersymmetric gauge field theory, independently as well as in the context of the holographic duality.The first part of the thesis is devoted to classical integrability and, in particular, to certain methods of analytic non-integrability, which are employed on various supergravity vacua. In Chapter 1, we introduce those tools of non-integrability, which consist of choosing an appro-priate string embedding and using differential Galois theory on the associated Hamiltonian system. The arena of all this, for the first chapter, is two classes of vacua in massive Type IIA supergravity, all of which are proven to be non-integrable, up to the trivial cases where the vacuum reduces to the Abelian and non-Abelian T-dual of known integrable backgrounds. Differential Galois theory, in this context, reduces to an algebraic form through Kovacic’s theorem, the proper use of which, on parametrized differential equations, is clarified in this application.In Chapter 2, we study integrability on the supergravity vacuum dual to the field-theoretical Ω-deformation of super Yang-Mills theory. The deformation manifests itself as turning on a Kalb-Ramond field on the dual supergravity vacuum and, by constructing appropriate string embeddings, we show that this space exhibits non-integrable dynamics. This, in turn, suggests that the Ω-deformation does not preserve classical integrability.In Chapter 3, we explore integrability on vacua in massive Type IIA supergravity, dual to six-dimensional superconformal quiver field theories. Analytic non-integrability illustrates that all vacua with a warped geometry, between Anti-de-Sitter space and the internal man-ifold, exhibit complete non-integrability, while in the special case of the unwarped space we prove the opposite to be true. In particular, we show that, besides the integrable dynamics on the symmetric Anti-de-Sitter subspace of the unwarped geometry, the σ-model on the internal manifold is an integrable deformation of the same model on the symmetric three-sphere, ultimately implying classical integrability of bosonic string theory on this special vacuum.The second part of the thesis is devoted to holography and, in particular, the AdS/CFT duality, which we exploit to study features of certain supersymmetric quantum field theories in two spacetime dimensions. More precisely, in Chapter 4, the final chapter, we study the duality between massive Type IIA supergravity vacua and two-dimensional quiver structures. After categorizing all kinds of gravity solutions, we demystify the ones that seem to reflect anomalous gauge theories. In particular, we prove that there are bound states of D-branes on the boundary of the space which provide the dual quiver theory with exactly the correct amount of matter in order to cancel its gauge anomalies. We also propose that the structure of the field theory should be complemented with additional bifundamental matter and, finally, we construct a BPS string configuration and use the old and new supersymmetric matter to build its dual ultraviolet operator
Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
No full textWe consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x = 0 and t = T < ∞, for space dimension N = 3,4,5,6. These solutions exhibit fast blow-up; i.e. they satisfy lim(t up arrowT)(T - t)(1/(p-1))u(0, t) = ∞. In contrast, radial solutions that are positive and decreasing behave as in the subcritical case for any N ≥ 3. This last result is extended in the case of exponential nonlinearity and N = 2.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEpu
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