10,764 research outputs found
Thermodynamics of Magnetised Kerr-Newman Black Holes
The thermodynamics of a magnetised Kerr-Newman black hole is studied to all
orders in the appended magnetic field . The asymptotic properties of the
metric and other fields are dominated by the magnetic flux that extends to
infinity along the axis, leading to subtleties in the calculation of conserved
quantities such as the angular momentum and the mass. We present a detailed
discussion of the implementation of a Wald-type procedure to calculate the
angular momentum, showing how ambiguities that are absent in the usual
asymptotically-flat case may be resolved by the requirement of gauge
invariance. We also present a formalism from which we are able to obtain an
expression for the mass of the magnetised black holes. The expressions for the
mass and the angular momentum are shown to be compatible with the first law of
thermodynamics and a Smarr type relation. Allowing the appended magnetic field
to vary results in an extra term in the first law of the form
where is interpreted as an induced magnetic moment. Minimising the total
energy with respect to the total charge at fixed values of the angular
momentum and energy of the seed metric allows an investigation of Wald's
process. The Meissner effect is shown to hold for electrically neutral extreme
black holes. We also present a derivation of the angular momentum for black
holes in the four-dimensional STU model, which is supergravity
coupled to three vector multiplets.Comment: 27 page
Structure of a model TiO2 photocatalytic interface
The interaction of water with TiO2 is crucial to many of its practical
applications, including photocatalytic water splitting. Following the first
demonstration of this phenomenon 40 years ago there have been numerous studies
of the rutile single-crystal TiO2(110) interface with water. This has provided
an atomic-level understanding of the water-TiO2 interaction. However, nearly
all of the previous studies of water/TiO2 interfaces involve water in the
vapour phase. Here, we explore the interfacial structure between liquid water
and a rutile TiO2(110) surface pre-characterized at the atomic level. Scanning
tunnelling microscopy and surface X-ray diffraction are used to determine the
structure, which is comprised of an ordered array of hydroxyl molecules with
molecular water in the second layer. Static and dynamic density functional
theory calculations suggest that a possible mechanism for formation of the
hydroxyl overlayer involves the mixed adsorption of O2 and H2O on a partially
defected surface. The quantitative structural properties derived here provide a
basis with which to explore the atomistic properties and hence mechanisms
involved in TiO2 photocatalysis
Nonlinear modes and symmetry breaking in rotating double-well potentials
We study modes trapped in a rotating ring carrying the self-focusing (SF) or
defocusing (SDF) cubic nonlinearity and double-well potential , where is the angular coordinate. The model, based on the nonlinear
Schr\"{o}dinger (NLS) equation in the rotating reference frame, describes the
light propagation in a twisted pipe waveguide, as well as in other optical
settings, and also a Bose-Einstein condensate (BEC)trapped in a torus and
dragged by the rotating potential. In the SF and SDF regimes, five and four
trapped modes of different symmetries are found, respectively. The shapes and
stability of the modes, and transitions between them are studied in the first
rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions
are found, of subcritical and supercritical types. In the SDF regime, an
antisymmetry-breaking transition occurs. Ground-states are identified in both
the SF and SDF systems.Comment: Physical Review A, in pres
Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing
We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic
equations with stochastic forcing, which are heterogeneous (i.e., not
space-translational invariant). A unified framework is established for the
continuous dependence estimates, fractional BV regularity estimates, and
well-posedness for stochastic entropy solutions of the nonlinear stochastic
degenerate parabolic-hyperbolic equation. In particular, we establish the
well-posedness of the nonlinear stochastic equation in
for and the --Nikolskii space with
, and the continuous dependence of the stochastic entropy
solutions not only on the initial data, but also on the degenerate diffusion
matrix function, the flux function, and the multiplicative noise function
involving in the nonlinear equation.Comment: 30 page
Quantum integrable system with two color components in two dimensions
The Davey-Stewartson 1(DS1) system[9] is an integrable model in two
dimensions. A quantum DS1 system with 2 colour-components in two dimensions has
been formulated. This two-dimensional problem has been reduced to two
one-dimensional many-body problems with 2 colour-components. The solutions of
the two-dimensional problem under consideration has been constructed from the
resulting problems in one dimensions. For latters with the -function
interactions and being solved by the Bethe ansatz, we introduce symmetrical and
antisymmetrical Young operators of the permutation group and obtain the exact
solutions for the quantum DS1 system. The application of the solusions is
discussed.Comment: 14 pages, LaTeX fil
Ordered Carboxylates on TiO (110) Formed at Aqueous Interfaces
As models for probing the interactions between TiO2 surfaces and the dye molecules employed in dye-sensitized solar cells, carboxylic acids are an important class of molecules. In this work we present a scanning tunneling microscopy (STM) and low energy electron diffraction (LEED)
study of three small carboxylic acids (formic, acetic, and benzoic) that were reacted with the TiO2(110) surface via a dipping procedure. The three molecules display quite different adsorption behavior, illustrating the different inter-adsorbate interactions that can occur. After
exposure to a 10 mM solution, formic acid forms a rather disordered formate overlayer with two distinct binding geometries. Acetic acid forms a well-ordered (2 × 1) acetate overlayer similar to that observed following deposition from vapor. Benzoic acid forms a (2 × 2) overlayer which is stabilized by intermolecular interactions between the phenyl groups
Normal families and fixed points of iterates
Let F be a family of holomorphic functions and let K be a constant less than
4. Suppose that for all f in F the second iterate of f does not have fixed
points for which the modulus of the multiplier is greater than K. We show that
then F is normal. This is deduced from a result about the multipliers of
iterated polynomials.Comment: 5 page
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