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### Shedding light on surfaces: using photons to transform and pattern material surfaces

The ultimate goal of surface modification is to quantitatively control surface properties by precise manipulation of surface chemical structure at the molecular level. Advances in the understanding of molecular design principles for soft matter surfaces can be combined with the available arsenal of interesting photochemical reactions to create an exciting paradigm for surface modification: the use of photons to both transform and pattern chemical functionality at soft matter surfaces. The success of the paradigm is predicated on the ability to design and synthesize "photochemical surface delivery vehicles," complex photoactive molecules that form stable surface monolayers and subsequently deliver photoactive moieties to the surface. Shedding light onto these smart, modified surfaces brings about a wide variety of precise photochemical reactions that are preprogrammed within the surface delivery vehicle. Surface chemical patterns are formed by exposure through a mask. Some photochemical surface transformation can be considered as "green" chemistry since only photons are required as reagents. In this review, we provide a brief tutorial on photochemistry fundamentals to illustrate the nature of possible photochemical surface reactions and discuss the principles of design for photochemical surface delivery vehicles. Applications of the paradigm drawn from a variety of fields emphasize the tremendous potential for photochemical surface transformation and patterning on both hard and soft substrates

### Towards Dynamic Control of Wettability by Using Functionalized Altitudinal Molecular Motors on Solid Surfaces

We report the synthesis of altitudinal molecular motors that contain functional groups in their rotor part. In an approach to achieve dynamic control over the properties of solid surfaces, a hydrophobic perfluorobutyl chain and a relatively hydrophilic cyano group were introduced to the rotor part of the motors. Molecular motors were attached to quartz surfa-ces by using interfacial 1,3-dipolar cycloadditions. To test the effect of the functional groups on the rotary motion, photochemical and thermal isomerization studies of the motors were per-formed both in solution and when attached to the surface. We found that the substituents have no significant effect on the thermal and photochemical processes, and the functionalized motors preserved their rotary function both in solution and on a quartz surface. Preliminary results on the influence of the functional groups on surface wettability are also described

### Codimension Two Compactifications and the Cosmological Constant Problem

We consider solutions of six dimensional Einstein equations with two compact
dimensions. It is shown that one can introduce 3-branes in this background in
such a way that the effective four dimensional cosmological constant is
completely independent of the brane tensions. These tensions are completely
arbitrary, without requiring any fine tuning. We must, however, fine tune bulk
parameters in order to obtain a sufficiently small value for the observable
cosmological constant. We comment in the effective four dimensional description
of this effect at energies below the compactification scale.Comment: 4 pages, rextex

### No Time Machine Construction in Open 2+1 Gravity with Timelike Total Energy Momentum

It is shown that in 2+1 dimensional gravity an open spacetime with timelike
sources and total energy momentum cannot have a stable compactly generated
Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and
shows, in particular, that not only a Gott pair cannot be formed from processes
such as the decay of a single cosmic string as has been shown by Carroll et
al., but that, in a precise sense, a time machine cannot be constructed at all.Comment: 7 pages. Several changes and 3 figures added. To appear in Phys. Rev.

### Exact Black Holes and Gravitational Shockwaves on Codimension-2 Branes

We derive exact gravitational fields of a black hole and a relativistic
particle stuck on a codimension-2 brane in $D$ dimensions when gravity is ruled
by the bulk $D$-dimensional Einstein-Hilbert action. The black hole is locally
the higher-dimensional Schwarzschild solution, which is threaded by a tensional
brane yielding a deficit angle and includes the first explicit example of a
`small' black hole on a tensional 3-brane. The shockwaves allow us to study the
large distance limits of gravity on codimension-2 branes. In an infinite
locally flat bulk, they extinguish as $1/r^{D-4}$, i.e. as $1/r^2$ on a 3-brane
in $6D$, manifestly displaying the full dimensionality of spacetime. We check
that when we compactify the bulk, this special case correctly reduces to the 4D
Aichelburg-Sexl solution at large distances. Our examples show that gravity
does not really obstruct having general matter stress-energy on codimension-2
branes, although its mathematical description may be more involved.Comment: 18 pages, LaTeX; v2: added references, version to appear in JHE

### Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory

It has been suggested that the observed value of the cosmological constant is
related to the supersymmetry breaking scale M_{susy} through the formula Lambda
\sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally
arises in the codimension two solutions of warped space-time varying
compactifications of string theory in which non-isotropic stringy moduli induce
a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map
between deSitter and global cosmic brane solutions clarified, supersymmetry
breaking discussion improved and references adde

### Cosmology of codimension-two braneworlds

We present a comprehensive study of the cosmological solutions of 6D
braneworld models with azimuthal symmetry in the extra dimensions, moduli
stabilization by flux or a bulk scalar field, and which contain at least one
3-brane that could be identified with our world. We emphasize an unusual
property of these models: their expansion rate depends on the 3-brane tension
either not at all, or in a nonstandard way, at odds with the naive expected
dimensional reduction of these systems to 4D general relativity at low
energies. Unlike other braneworld attempts to find a self-tuning solution to
the cosmological constant problem, the apparent failure of decoupling in these
models is not associated with the presence of unstabilized moduli; rather it is
due to automatic cancellation of the brane tension by the curvature induced by
the brane. This provides some corroboration for the hope that these models
provide a distinctive step toward understanding the smallness of the observed
cosmological constant. However, we point out some challenges for obtaining
realistic cosmology within this framework.Comment: 30 pages, 4 figures; generalized result for nonconventional Friedmann
equation, added referenc

### Disappearing Dark Matter in Brane World Cosmology: New Limits on Noncompact Extra Dimensions

We explore cosmological implications of dark matter as massive particles
trapped on a brane embedded in a Randall-Sundrum noncompact higher dimension
$AdS_5$ space. It is an unavoidable consequence of this cosmology that massive
particles are metastable and can disappear into the bulk dimension. Here, we
show that a massive dark matter particle (e.g. the lightest supersymmetric
particle) is likely to have the shortest lifetime for disappearing into the
bulk. We examine cosmological constraints on this new paradigm and show that
disappearing dark matter is consistent (at the 95% confidence level) with all
cosmological constraints, i.e. present observations of Type Ia supernovae at
the highest redshift, trends in the mass-to-light ratios of galaxy clusters
with redshift, the fraction of X-ray emitting gas in rich clusters, and the
spectrum of power fluctuations in the cosmic microwave background. A best $2
\sigma$ concordance region is identified corresponding to a mean lifetime for
dark matter disappearance of $15 \le \Gamma^{-1} \le 80$ Gyr. The implication
of these results for brane-world physics is discussed.Comment: 7 pages, 7 figures, new cosmological constraints added, accepted for
publication in PR

### BPS Domain Walls in Large N Supersymmetric QCD

We explicitly construct BPS domain walls interpolating between neighboring
chirally asymmetric vacua in a model for large N pure supersymmetric QCD. The
BPS equations for the corresponding ${\bf Z}_N$ symmetric order parameter
effective Lagrangian reduce to those in the $A_N$ Landau-Ginsburg model
assuming that the higher derivative terms in the K{\"a}hler potential are
suppressed in the large N limit. These BPS domain walls, which have vanishing
width in the large N limit, can be viewed as supermembranes embedded in a
(3+1)-dimensional supersymmetric QCD background. The supermembrane couples to a
three-form supermultiplet whose components we identify with the composite
fields of supersymmetric QCD. We also discuss certain aspects of chromoelectric
flux tubes (open strings) ending on these walls which appear to support their
interpretation as D-branes.Comment: 24 REVTEX pages. Journal version. Comments added, typos correcte

### Non stationary Einstein-Maxwell fields interacting with a superconducting cosmic string

Non stationary cylindrically symmetric exact solutions of the
Einstein-Maxwell equations are derived as single soliton perturbations of a
Levi-Civita metric, by an application of Alekseev inverse scattering method. We
show that the metric derived by L. Witten, interpreted as describing the
electrogravitational field of a straight, stationary, conducting wire may be
recovered in the limit of a `wide' soliton. This leads to the possibility of
interpreting the solitonic solutions as representing a non stationary
electrogravitational field exterior to, and interacting with, a thin, straight,
superconducting cosmic string. We give a detailed discussion of the
restrictions that arise when appropiate energy and regularity conditions are
imposed on the matter and fields comprising the string, considered as `source',
the most important being that this `source' must necessarily have a non-
vanishing minimum radius. We show that as a consequence, it is not possible,
except in the stationary case, to assign uniquely a current to the source from
a knowledge of the electrogravitational fields outside the source. A discussion
of the asymptotic properties of the metrics, the physical meaning of their
curvature singularities, as well as that of some of the metric parameters, is
also included.Comment: 14 pages, no figures (RevTex

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