2,974 research outputs found
Diversity and Security in UK Electricity Generation: The Influence of Low Carbon Objectives
We explore the relationship between low carbon objectives and the strategic security of electricity in the context of the UK Electricity System. We consider diversity of fuel source mix to represent one dimension of security - robustness against interruptions of any one source - and apply two different diversity indices to the range of electricity system scenarios produced by the UK government and independent researchers. Using data on wind generation we also consider whether a second dimension of security - the reliability of generation availability - is compromised by intermittency of renewable generation. Our results show that low carbon objectives are uniformly associated with greater long-term diversity in UK electricity. We discuss reasons for this result, explore sensitivities, and briefly discuss possible policy instruments associated with diversity and their limitations.Diversity, Security, Low Carbon, Wind Generation, Electricity
Dirac Operator on a disk with global boundary conditions
We compute the functional determinant for a Dirac operator in the presence of
an Abelian gauge field on a bidimensional disk, under global boundary
conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the
connection between our result and the index theorem.Comment: RevTeX, 11 pages. References adde
Smeared heat-kernel coefficients on the ball and generalized cone
We consider smeared zeta functions and heat-kernel coefficients on the
bounded, generalized cone in arbitrary dimensions. The specific case of a ball
is analysed in detail and used to restrict the form of the heat-kernel
coefficients on smooth manifolds with boundary. Supplemented by conformal
transformation techniques, it is used to provide an effective scheme for the
calculation of the . As an application, the complete coefficient
is given.Comment: 23 pages, JyTe
Global Theory of Quantum Boundary Conditions and Topology Change
We analyze the global theory of boundary conditions for a constrained quantum
system with classical configuration space a compact Riemannian manifold
with regular boundary . The space \CM of self-adjoint
extensions of the covariant Laplacian on is shown to have interesting
geometrical and topological properties which are related to the different
topological closures of . In this sense, the change of topology of is
connected with the non-trivial structure of \CM. The space \CM itself can
be identified with the unitary group \CU(L^2(\Gamma,\C^N)) of the Hilbert
space of boundary data L^2(\Gamma,\C^N). A particularly interesting family of
boundary conditions, identified as the set of unitary operators which are
singular under the Cayley transform, \CC_-\cap \CC_+ (the Cayley manifold),
turns out to play a relevant role in topology change phenomena. The singularity
of the Cayley transform implies that some energy levels, usually associated
with edge states, acquire an infinity energy when by an adiabatic change the
boundary condition reaches the Cayley submanifold \CC_-. In this sense
topological transitions require an infinite amount of quantum energy to occur,
although the description of the topological transition in the space \CM is
smooth. This fact has relevant implications in string theory for possible
scenarios with joint descriptions of open and closed strings. In the particular
case of elliptic self--adjoint boundary conditions, the space \CC_- can be
identified with a Lagrangian submanifold of the infinite dimensional
Grassmannian. The corresponding Cayley manifold \CC_- is dual of the Maslov
class of \CM.Comment: 29 pages, 2 figures, harvma
Determinants of Dirac operators with local boundary conditions
We study functional determinants for Dirac operators on manifolds with
boundary. We give, for local boundary conditions, an explicit formula relating
these determinants to the corresponding Green functions. We finally apply this
result to the case of a bidimensional disk under bag-like conditions.Comment: standard LaTeX, 24 pages. To appear in Jour. Math. Phy
Fractional-order operators: Boundary problems, heat equations
The first half of this work gives a survey of the fractional Laplacian (and
related operators), its restricted Dirichlet realization on a bounded domain,
and its nonhomogeneous local boundary conditions, as treated by
pseudodifferential methods. The second half takes up the associated heat
equation with homogeneous Dirichlet condition. Here we recall recently shown
sharp results on interior regularity and on -estimates up to the boundary,
as well as recent H\"older estimates. This is supplied with new higher
regularity estimates in -spaces using a technique of Lions and Magenes,
and higher -regularity estimates (with arbitrarily high H\"older estimates
in the time-parameter) based on a general result of Amann. Moreover, it is
shown that an improvement to spatial -regularity at the boundary is
not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in
Mathematics and Statistics: "New Perspectives in Mathematical Analysis -
Plenary Lectures, ISAAC 2017, Vaxjo Sweden
Ellipticity Conditions for the Lax Operator of the KP Equations
The Lax pseudo-differential operator plays a key role in studying the general
set of KP equations, although it is normally treated in a formal way, without
worrying about a complete characterization of its mathematical properties. The
aim of the present paper is therefore to investigate the ellipticity condition.
For this purpose, after a careful evaluation of the kernel with the associated
symbol, the majorization ensuring ellipticity is studied in detail. This leads
to non-trivial restrictions on the admissible set of potentials in the Lax
operator. When their time evolution is also considered, the ellipticity
conditions turn out to involve derivatives of the logarithm of the
tau-function.Comment: 21 pages, plain Te
Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
We consider the hamiltonian operator associated with planar sec- tions of
infinitely long cylindrical solenoids and with a homogeneous magnetic field in
their interior. First, in the Sobolev space , we characterize all
generalized boundary conditions on the solenoid bor- der compatible with
quantum mechanics, i.e., the boundary conditions so that the corresponding
hamiltonian operators are self-adjoint. Then we study and compare the
scattering of the most usual boundary con- ditions, that is, Dirichlet, Neumann
and Robin.Comment: 40 pages, 5 figure
The hybrid spectral problem and Robin boundary conditions
The hybrid spectral problem where the field satisfies Dirichlet conditions
(D) on part of the boundary of the relevant domain and Neumann (N) on the
remainder is discussed in simple terms. A conjecture for the C_1 coefficient is
presented and the conformal determinant on a 2-disc, where the D and N regions
are semi-circles, is derived. Comments on higher coefficients are made.
A hemisphere hybrid problem is introduced that involves Robin boundary
conditions and leads to logarithmic terms in the heat--kernel expansion which
are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added.
Substantial Robin additions. Substantial revisio
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