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