1,451 research outputs found
Energy-momentum diffusion from spacetime discreteness
We study potentially observable consequences of spatiotemporal discreteness
for the motion of massive and massless particles. First we describe some simple
intrinsic models for the motion of a massive point particle in a fixed causal
set background. At large scales, the microscopic swerves induced by the
underlying atomicity manifest themselves as a Lorentz invariant diffusion in
energy-momentum governed by a single phenomenological parameter, and we derive
in full the corresponding diffusion equation. Inspired by the simplicity of the
result, we then derive the most general Lorentz invariant diffusion equation
for a massless particle, which turns out to contain two phenomenological
parameters describing, respectively, diffusion and drift in the particle's
energy. The particles do not leave the light cone however: their worldlines
continue to be null geodesics. Finally, we deduce bounds on the drift and
diffusion constants for photons from the blackbody nature of the spectrum of
the cosmic microwave background radiation.Comment: 13 pages, 4 figures, corrected minor typos and updated to match
published versio
Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle
There ought to exist a reformulation of quantum mechanics which does not
refer to an external classical spacetime manifold. Such a reformulation can be
achieved using the language of noncommutative differential geometry. A
consequence which follows is that the `weakly quantum, strongly gravitational'
dynamics of a relativistic particle whose mass is much greater than Planck mass
is dual to the `strongly quantum, weakly gravitational' dynamics of another
particle whose mass is much less than Planck mass. The masses of the two
particles are inversely related to each other, and the product of their masses
is equal to the square of Planck mass. This duality explains the observed value
of the cosmological constant, and also why this value is nonzero but extremely
small in Planck units.Comment: 7 pages. Second Prize in Gravity Research Foundation Essay
Competition, 2008. Two paragraphs added to original essay to enhance clarity.
To appear in Gen. Rel. Gra
Stable non-uniform black strings below the critical dimension
The higher-dimensional vacuum Einstein equation admits translationally
non-uniform black string solutions. It has been argued that infinitesimally
non-uniform black strings should be unstable in 13 or fewer dimensions and
otherwise stable. We construct numerically non-uniform black string solutions
in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using
local Penrose inequalities. Weakly non-uniform solutions behave as expected.
However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be
stable and can have greater horizon area than a uniform string of the same
mass. In 14 and 15 dimensions all non-uniform black strings appear to be
stable.Comment: 26 pages, 11 figures. V2: reference added, matches published versio
Cosmological Constant and Noncommutative Spacetime
We show that the cosmological constant appears as a Lagrange multiplier if
nature is described by a canonical noncommutative spacetime. It is thus an
arbitrary parameter unrelated to the action and thus to vacuum fluctuations.
The noncommutative algebra restricts general coordinate transformations to
four-volume preserving noncommutative coordinate transformations. The
noncommutative gravitational action is thus an unimodular noncommutative
gravity. We show that spacetime noncommutativity provides a very natural
justification to an unimodular gravity solution to the cosmological problem. We
obtain the right order of magnitude for the critical energy density of the
universe if we assume that the scale for spacetime noncommutativity is the
Planck scale.Comment: 7 page
Why do we observe a small but non zero cosmological constant ?
The current observations seem to suggest that the universe has a positive
cosmological constant of the order of while the most natural value for
the cosmological constant will be where
is the Planck length. This reduction of the cosmological constant from
to may be interpreted as due to the ability of
quantum micro structure of spacetime to readjust itself and absorb bulk vacuum
energy densities. Being a quantum mechanical process, such a cancellation
cannot be exact and the residual quantum fluctuations appear as the ``small''
cosmological constant. I describe the features of a toy model for the spacetime
micro structure which could allow for the bulk vacuum energy densities to be
canceled leaving behind a small residual value of the the correct magnitude.
Some other models (like the ones based on canonical ensemble for the four
volume or quantum fluctuations of the horizon size) lead to an insignificantly
small value of with showing that obtaining the
correct order of magnitude for the residual fluctuations in the cosmological
constant is a nontrivial task, becaue of the existence of the small
dimensionless number .Comment: couple of references added; matches with published versio
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Development and validation of the Wesleyan Intercultural Competence Scale (WICS): A tool for measuring the impact of study abroad experiences.
As globalization becomes commonplace and the world becomes increasingly interconnected, institutions of higher education have begun to prioritize the development of intercultural competence in their students. A recent review of university statements of essential learning outcomes revealed that 85% of top-ranked National Universities in the U.S. and 68% of top-ranked Liberal Arts colleges in the U.S. stated that the development of intercultural competence is one of their primary objectives (Stemler, 2012). For National Universities this was the most frequently cited objective across the entire sample, edging out other priorities such as writing, quantitative reasoning, and information literacy. The importance of developing the intercultural competence of students has been emphasized by private-sector businesses as well. A 2010 study commissioned by the Association of American Colleges and Universities found that 67% of the 302 employers interviewed felt that the ability to understand the global context of situations and decisions was one of the most important aims of higher education (AAC&U, 2010)
WASH and Tsg101/ALIX-dependent diversion of stress-internalized EGFR from the canonical endocytic pathway
Stress exposure triggers ligand-independent EGF receptor (EGFR) endocytosis, but its post-endocytic fate and role in regulating signalling are unclear. We show that the p38 MAP kinase-dependent, EGFR tyrosine kinase (TK)-independent EGFR internalization induced by ultraviolet light C (UVC) or the cancer therapeutic cisplatin, is followed by diversion from the canonical endocytic pathway. Instead of lysosomal degradation or plasma membrane recycling, EGFR accumulates in a subset of LBPA-rich perinuclear multivesicular bodies (MVBs) distinct from those carrying EGF-stimulated EGFR. Stress-internalized EGFR co-segregates with exogenously expressed pre-melanosomal markers OA1 and fibrillar PMEL, following early endosomal sorting by the actin polymerization-promoting WASH complex. Stress-internalized EGFR is retained intracellularly by continued p38 activity in a mechanism involving ubiquitin-independent, ESCRT/ALIX-dependent incorporation onto intraluminal vesicles (ILVs) of MVBs. In contrast to the internalization-independent EGF-stimulated activation, UVC/cisplatin-triggered EGFR activation depends on EGFR internalization and intracellular retention. EGFR signalling from this MVB subpopulation delays apoptosis and might contribute to chemoresistance
Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
We describe the first convergent numerical method to determine static black
hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a
family of solutions parametrized by the ratio of the black hole size and the
size of the compact extra dimension. The solutions satisfy the demanding
integrated first law. For small black holes our solutions approach the 5d
Schwarzschild solution and agree very well with new theoretical predictions for
the small corrections to thermodynamics and geometry. The existence of such
black holes is thus established. We report on thermodynamical (temperature,
entropy, mass and tension along the compact dimension) and geometrical
measurements. Most interestingly, for large masses (close to the
Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as
evidence for an approach to a physical tachyonic instability. Using
extrapolation we speculate that the system undergoes a first order phase
transition.Comment: 42 pages, 19 eps figures; v2: 3 references added, version to appear
in Phys.Rev.
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory
In backgrounds with compact dimensions there may exist several phases of
black objects including the black-hole and the black-string. The phase
transition between them raises puzzles and touches fundamental issues such as
topology change, uniqueness and Cosmic Censorship. No analytic solution is
known for the black hole, and moreover, one can expect approximate solutions
only for very small black holes, while the phase transition physics happens
when the black hole is large. Hence we turn to numerical solutions. Here some
theoretical background to the numerical analysis is given, while the results
will appear in a forthcoming paper. Goals for a numerical analysis are set. The
scalar charge and tension along the compact dimension are defined and used as
improved order parameters which put both the black hole and the black string at
finite values on the phase diagram. Predictions for small black holes are
presented. The differential and the integrated forms of the first law are
derived, and the latter (Smarr's formula) can be used to estimate the ``overall
numerical error''. Field asymptotics and expressions for physical quantities in
terms of the numerical ones are supplied. Techniques include ``method of
equivalent charges'', free energy, dimensional reduction, and analytic
perturbation for small black holes.Comment: 23 pages. v3: version to be published in PRD, 3 references adde
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