15,868 research outputs found
Understanding the tsunami with a simple model
In this paper, we use the approximation of shallow water waves (Margaritondo
G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a
variable depth. We deduce the shallow water wave equation and the continuity
equation that must be satisfied when a wave encounters a discontinuity in the
sea depth. A short explanation about how the tsunami hit the west coast of
India is given based on the refraction phenomenon. Our procedure also includes
a simple numerical calculation suitable for undergraduate students in physics
and engineering
Locality, Causality and Noncommutative Geometry
We analyse the causality condition in noncommutative field theory and show
that the nonlocality of noncommutative interaction leads to a modification of
the light cone to the light wedge. This effect is generic for noncommutative
geometry. We also check that the usual form of energy condition is violated and
propose that a new form is needed in noncommutative spacetime. On reduction
from light cone to light wedge, it looks like the noncommutative dimensions are
effectively washed out and suggests a reformulation of noncommutative field
theory in terms of lower dimensional degree of freedom. This reduction of
dimensions due to noncommutative geometry could play a key role in explaining
the holographic property of quantum gravity.Comment: 16 pages, LaTeX, 4 figure
Random on-board pixel sampling (ROPS) X-ray Camera
Recent advances in compressed sensing theory and algorithms offer new
possibilities for high-speed X-ray camera design. In many CMOS cameras, each
pixel has an independent on-board circuit that includes an amplifier, noise
rejection, signal shaper, an analog-to-digital converter (ADC), and optional
in-pixel storage. When X-ray images are sparse, i.e., when one of the following
cases is true: (a.) The number of pixels with true X-ray hits is much smaller
than the total number of pixels; (b.) The X-ray information is redundant; or
(c.) Some prior knowledge about the X-ray images exists, sparse sampling may be
allowed. Here we first illustrate the feasibility of random on-board pixel
sampling (ROPS) using an existing set of X-ray images, followed by a discussion
about signal to noise as a function of pixel size. Next, we describe a possible
circuit architecture to achieve random pixel access and in-pixel storage. The
combination of a multilayer architecture, sparse on-chip sampling, and
computational image techniques, is expected to facilitate the development and
applications of high-speed X-ray camera technology.Comment: 9 pages, 6 figures, Presented in 19th iWoRI
Gauge and Supersymmetric Invariance of a Boundary Bagger-Lambert-Gustavsson Theory
In this paper we will discuss the effect of a having a boundary on the
supersymmetric invariance and gauge invariance of the Bagger-Lambert-Gustavsson
(BLG) Theory. We will show that even though the supersymmetry and gauge
invariance of the original BLG theory is broken due to the presence of a
boundary, it restored by the addition of suitable boundary terms. In fact, to
achieve the gauge invariance of this theory, we will have to introduce new
boundary degrees of freedom. The boundary theory obeyed by these new boundary
degrees of freedom will be shown to be a generalization of the gauged
Wess-Zumino-Witten model, with the generators of the Lie algebra replaced by
the generators of the Lie 3-algebra. The gauge and supersymmetry variations of
the boundary theory will exactly cancel the boundary terms generated by the
gauge and supersymmetric variations of the bulk theory.Comment: 15 pages, 0 figures, accepted for publication in JHE
Noncommutative Moduli for Multi-Instantons
There exists a recursive algorithm for constructing BPST-type
multi-instantons on commutative R^4. When deformed noncommutatively, however,
it becomes difficult to write down non-singular instanton configurations with
topological charge greater than one in explicit form. We circumvent this
difficulty by allowing for the translational instanton moduli to become
noncommutative as well. This makes possible the ADHM construction of 't Hooft
multi-instanton solutions with everywhere self-dual field strengths on
noncommutative R^4.Comment: 1+9 pages; v2: reference added, published versio
Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies
We study exact multi-soliton solutions of integrable hierarchies on
noncommutative space-times which are represented in terms of quasi-determinants
of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic
behavior of the multi-soliton solutions and found that the asymptotic
configurations in soliton scattering process can be all the same as commutative
ones, that is, the configuration of N-soliton solution has N isolated localized
energy densities and the each solitary wave-packet preserves its shape and
velocity in the scattering process. The phase shifts are also the same as
commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy
is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE
Comments on Noncommutative ADHM Construction
We extend the method of matrix partition to obtain explicitly the gauge field
for noncommutative ADHM construction in some general cases. As an application
of this method we apply it to the U(2) 2-instanton and get explicit result for
the gauge fields in the coincident instanton limit. We also easily apply it to
the noncommutative 't Hooft instantons in the appendix.Comment: 17 pages, LaTeX; an appendix added, typos corrected, refs adde
On the Non-invasive Measurement of the Intrinsic Quantum Hall Effect
With a model calculation, we demonstrate that a non-invasive measurement of
intrinsic quantum Hall effect defined by the local chemical potential in a
ballistic quantum wire can be achieved with the aid of a pair of voltage leads
which are separated by potential barriers from the wire. B\"uttiker's formula
is used to determine the chemical potential being measured and is shown to
reduce exactly to the local chemical potential in the limit of strong potential
confinement in the voltage leads. Conditions for quantisation of Hall
resistance and measuring local chemical potential are given.Comment: 16 pages LaTex, 2 post-script figures available on reques
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